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  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementNumberOfPlans_f5d0a552-e16e-4566-a469-f08c1c5d3738_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementNumberOfPlans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of plans</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Accrued Liabilities [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_9968d62b-3cee-43de-bf2f-b58965c362b1_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_d21b9ee9-71a3-4f86-b1d8-b8f88d7a5922_totalLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total accrued liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_AccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_23f78ac0-5d2d-4013-8dee-904acdece753_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RangeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeMember" xlink:to="lab_srt_RangeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryValuationReserves_d8440bbd-d151-4461-b4d6-28aa2fab4b0e_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryValuationReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reserve for excess or obsolete inventory</link:label>
    <link:label id="lab_us-gaap_InventoryValuationReserves_label_en-US" xlink:label="lab_us-gaap_InventoryValuationReserves" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory Valuation Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryValuationReserves" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryValuationReserves"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryValuationReserves" xlink:to="lab_us-gaap_InventoryValuationReserves" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpense_2a863e41-f39d-4be5-9b8a-73f065755ecb_terseLabel_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Research and development</link:label>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpense_label_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Research and Development Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResearchAndDevelopmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ResearchAndDevelopmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResearchAndDevelopmentExpense" xlink:to="lab_us-gaap_ResearchAndDevelopmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_d0704445-3e1a-42f3-8a76-deea4bcbab56_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Issuances</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Issuances</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_1e5484dd-c757-4ce0-b89d-d30a8d4728ab_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Changes in operating assets and liabilities:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Operating Capital [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInOperatingCapitalAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingCapitalAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays_79a5e691-16c0-4c11-a356-f67c9ecb0dfd_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of warrant or right, conversion terms, threshold trading days</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class Of Warrant Or Right, Conversion Terms, Threshold Trading Days</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class Of Warrant Or Right, Conversion Terms, Threshold Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:href="tlsi-20230930.xsd#tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:to="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockLiquidationPreference_92376e9c-c3e8-47c0-a38f-4a86fc395a9d_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liquidation preference (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockLiquidationPreference_label_en-US" xlink:label="lab_us-gaap_PreferredStockLiquidationPreference" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Liquidation Preference Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockLiquidationPreference" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockLiquidationPreference"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockLiquidationPreference" xlink:to="lab_us-gaap_PreferredStockLiquidationPreference" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_39742642-4373-44f4-beec-e48c1d066290_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Award Type [Domain]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues_9bc3ef05-f794-4f9f-86f7-63fcb82e8168_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Issuances</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Temporary Equity, Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_TemporaryEquityStockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_GuidelinePublicCompanyModelMember_20e26bc3-ad82-4a47-bcb5-7095b0f0da28_terseLabel_en-US" xlink:label="lab_tlsi_GuidelinePublicCompanyModelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Guideline Public Company Model</link:label>
    <link:label id="lab_tlsi_GuidelinePublicCompanyModelMember_label_en-US" xlink:label="lab_tlsi_GuidelinePublicCompanyModelMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Guideline Public Company Model [Member]</link:label>
    <link:label id="lab_tlsi_GuidelinePublicCompanyModelMember_documentation_en-US" xlink:label="lab_tlsi_GuidelinePublicCompanyModelMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Guideline Public Company Model</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_GuidelinePublicCompanyModelMember" xlink:href="tlsi-20230930.xsd#tlsi_GuidelinePublicCompanyModelMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_GuidelinePublicCompanyModelMember" xlink:to="lab_tlsi_GuidelinePublicCompanyModelMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ProceedsFromReverseRecapitalizationTransaction_359ce391-b1fb-48c5-a00d-abda67a9f322_totalLabel_en-US" xlink:label="lab_tlsi_ProceedsFromReverseRecapitalizationTransaction" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from transaction</link:label>
    <link:label id="lab_tlsi_ProceedsFromReverseRecapitalizationTransaction_label_en-US" xlink:label="lab_tlsi_ProceedsFromReverseRecapitalizationTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds From Reverse Recapitalization Transaction</link:label>
    <link:label id="lab_tlsi_ProceedsFromReverseRecapitalizationTransaction_documentation_en-US" xlink:label="lab_tlsi_ProceedsFromReverseRecapitalizationTransaction" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds From Reverse Recapitalization Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ProceedsFromReverseRecapitalizationTransaction" xlink:href="tlsi-20230930.xsd#tlsi_ProceedsFromReverseRecapitalizationTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ProceedsFromReverseRecapitalizationTransaction" xlink:to="lab_tlsi_ProceedsFromReverseRecapitalizationTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommercialMilestone1000000AnnualSalesMember_88cd0be4-569b-4aae-ad2f-2ad07f6b6096_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestone1000000AnnualSalesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, $1,000,000 Annual Sales</link:label>
    <link:label id="lab_tlsi_CommercialMilestone1000000AnnualSalesMember_label_en-US" xlink:label="lab_tlsi_CommercialMilestone1000000AnnualSalesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, $1,000,000 Annual Sales [Member]</link:label>
    <link:label id="lab_tlsi_CommercialMilestone1000000AnnualSalesMember_documentation_en-US" xlink:label="lab_tlsi_CommercialMilestone1000000AnnualSalesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, $1,000,000 Annual Sales</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestone1000000AnnualSalesMember" xlink:href="tlsi-20230930.xsd#tlsi_CommercialMilestone1000000AnnualSalesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommercialMilestone1000000AnnualSalesMember" xlink:to="lab_tlsi_CommercialMilestone1000000AnnualSalesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_NatureOfBusinessLineItems_0f00ebbb-f63d-4409-8185-4f6e748b4891_terseLabel_en-US" xlink:label="lab_tlsi_NatureOfBusinessLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Nature of Business [Line Items]</link:label>
    <link:label id="lab_tlsi_NatureOfBusinessLineItems_label_en-US" xlink:label="lab_tlsi_NatureOfBusinessLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Nature of Business [Line Items]</link:label>
    <link:label id="lab_tlsi_NatureOfBusinessLineItems_documentation_en-US" xlink:label="lab_tlsi_NatureOfBusinessLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Nature of Business [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_NatureOfBusinessLineItems" xlink:href="tlsi-20230930.xsd#tlsi_NatureOfBusinessLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_NatureOfBusinessLineItems" xlink:to="lab_tlsi_NatureOfBusinessLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ScheduleOfReverseRecapitalizationTable_ef0d3015-4715-4ca6-ad04-08d5fc39eeea_terseLabel_en-US" xlink:label="lab_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Reverse Recapitalization [Table]</link:label>
    <link:label id="lab_tlsi_ScheduleOfReverseRecapitalizationTable_label_en-US" xlink:label="lab_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Reverse Recapitalization [Table]</link:label>
    <link:label id="lab_tlsi_ScheduleOfReverseRecapitalizationTable_documentation_en-US" xlink:label="lab_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:href="tlsi-20230930.xsd#tlsi_ScheduleOfReverseRecapitalizationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:to="lab_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_5d350b08-eba2-475c-81eb-f42d38f98064_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitments and contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_d75c126d-fc61-4ed3-82c9-27506ac0812f_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expected share price volatility</link:label>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Input, Price Volatility [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputPriceVolatilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputPriceVolatilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputPriceVolatilityMember" xlink:to="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfWarrants_d4fc554c-f032-44dc-8bec-e0c1fcda11a6_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfWarrants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for repurchase of warrants</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfWarrants_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfWarrants" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for Repurchase of Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfWarrants" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsForRepurchaseOfWarrants"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfWarrants" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfWarrants" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SaleOfStockNumberOfSharesIssuedInTransactionPotentialIncreasedAmount_39ee3f58-d1e3-4c93-9321-929adc54e237_terseLabel_en-US" xlink:label="lab_tlsi_SaleOfStockNumberOfSharesIssuedInTransactionPotentialIncreasedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of shares issued in transaction, potential increased amount (in shares)</link:label>
    <link:label id="lab_tlsi_SaleOfStockNumberOfSharesIssuedInTransactionPotentialIncreasedAmount_label_en-US" xlink:label="lab_tlsi_SaleOfStockNumberOfSharesIssuedInTransactionPotentialIncreasedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction, Potential Increased Amount</link:label>
    <link:label id="lab_tlsi_SaleOfStockNumberOfSharesIssuedInTransactionPotentialIncreasedAmount_documentation_en-US" xlink:label="lab_tlsi_SaleOfStockNumberOfSharesIssuedInTransactionPotentialIncreasedAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction, Potential Increased Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SaleOfStockNumberOfSharesIssuedInTransactionPotentialIncreasedAmount" xlink:href="tlsi-20230930.xsd#tlsi_SaleOfStockNumberOfSharesIssuedInTransactionPotentialIncreasedAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SaleOfStockNumberOfSharesIssuedInTransactionPotentialIncreasedAmount" xlink:to="lab_tlsi_SaleOfStockNumberOfSharesIssuedInTransactionPotentialIncreasedAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_MTACWarrantsMember_44847da0-3b8f-45e6-9854-b1cc35264e0e_terseLabel_en-US" xlink:label="lab_tlsi_MTACWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">MTAC Warrants</link:label>
    <link:label id="lab_tlsi_MTACWarrantsMember_label_en-US" xlink:label="lab_tlsi_MTACWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">MTAC Warrants [Member]</link:label>
    <link:label id="lab_tlsi_MTACWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_MTACWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">MTAC Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_MTACWarrantsMember" xlink:href="tlsi-20230930.xsd#tlsi_MTACWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_MTACWarrantsMember" xlink:to="lab_tlsi_MTACWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume_9d37377d-2a87-4286-846d-0d69f9a9d083_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase agreement, maximum shares allowed, percentage of average daily volume</link:label>
    <link:label id="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume_label_en-US" xlink:label="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock, Share Price, Percentage Of Average Daily Volume</link:label>
    <link:label id="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume_documentation_en-US" xlink:label="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock, Share Price, Percentage Of Average Daily Volume</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:href="tlsi-20230930.xsd#tlsi_CommonStockSharePricePercentageOfAverageDailyVolume"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:to="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_dd4c3f82-6cee-4595-b066-233d36d7163a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Tax Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeTaxDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureTextBlock" xlink:to="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_GainLossOnWarrantExpirations_5b8d4547-da3f-475f-8c9f-8c1bc6a417c3_negatedTerseLabel_en-US" xlink:label="lab_tlsi_GainLossOnWarrantExpirations" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gain on expired warrants</link:label>
    <link:label id="lab_tlsi_GainLossOnWarrantExpirations_label_en-US" xlink:label="lab_tlsi_GainLossOnWarrantExpirations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gain (Loss) on Warrant Expirations</link:label>
    <link:label id="lab_tlsi_GainLossOnWarrantExpirations_documentation_en-US" xlink:label="lab_tlsi_GainLossOnWarrantExpirations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gain (Loss) on Warrant Expirations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_GainLossOnWarrantExpirations" xlink:href="tlsi-20230930.xsd#tlsi_GainLossOnWarrantExpirations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_GainLossOnWarrantExpirations" xlink:to="lab_tlsi_GainLossOnWarrantExpirations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_39337a76-61e0-40c2-8f06-93c24e58feb1_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Leases</link:label>
    <link:label id="lab_us-gaap_LesseeLeasesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lessee, Leases [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LesseeLeasesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeLeasesPolicyTextBlock" xlink:to="lab_us-gaap_LesseeLeasesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SeriesBConvertiblePreferredStockMember_f2dcfc4f-8951-48e5-a2c2-63fda50ddbdb_terseLabel_en-US" xlink:label="lab_tlsi_SeriesBConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B</link:label>
    <link:label id="lab_tlsi_SeriesBConvertiblePreferredStockMember_label_en-US" xlink:label="lab_tlsi_SeriesBConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_tlsi_SeriesBConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_tlsi_SeriesBConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SeriesBConvertiblePreferredStockMember" xlink:href="tlsi-20230930.xsd#tlsi_SeriesBConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SeriesBConvertiblePreferredStockMember" xlink:to="lab_tlsi_SeriesBConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_f9e63876-4a6a-48c6-9352-131557fd56ab_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current liabilities:</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrentAbstract" xlink:to="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_31be8d2b-bc10-43ba-a277-0adad465aa22_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockValue_c66d4645-9a1f-45db-8b99-c0a72527123e_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock, Series A, $0.0001 par value per share, $10.00 liquidation value per share. Authorized 10,000,000 and 0 shares at September&#160;30, 2023, and December&#160;31, 2022, respectively; issued and outstanding, 4,015,002 and 0 shares at September&#160;30, 2023, and December&#160;31, 2022, respectively</link:label>
    <link:label id="lab_us-gaap_PreferredStockValue_label_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockValue" xlink:to="lab_us-gaap_PreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PaymentsForAssetAcquisition_fc518c6f-12fc-4f24-90d7-0bcaee0f1a47_terseLabel_en-US" xlink:label="lab_tlsi_PaymentsForAssetAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payment for asset acquisition</link:label>
    <link:label id="lab_tlsi_PaymentsForAssetAcquisition_label_en-US" xlink:label="lab_tlsi_PaymentsForAssetAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for Asset Acquisition</link:label>
    <link:label id="lab_tlsi_PaymentsForAssetAcquisition_documentation_en-US" xlink:label="lab_tlsi_PaymentsForAssetAcquisition" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for Asset Acquisition</link:label>
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    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_3af3387f-89b6-45aa-9b81-99c7bed129a9_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeDomain" xlink:to="lab_us-gaap_SubsequentEventTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_cf026151-8b0b-4c10-af57-0c15ade3faf7_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Recurring and Nonrecurring [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable"/>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_6ad0c74c-03b8-4d60-b007-5f8998c6a9aa_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
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    <link:label id="lab_tlsi_SeriesB2TrancheLiabilityMember_725d7a8d-b93c-4206-a88a-9cc05dc1f7d0_terseLabel_en-US" xlink:label="lab_tlsi_SeriesB2TrancheLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B-2 Tranche Liability</link:label>
    <link:label id="lab_tlsi_SeriesB2TrancheLiabilityMember_label_en-US" xlink:label="lab_tlsi_SeriesB2TrancheLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B-2 Tranche Liability [Member]</link:label>
    <link:label id="lab_tlsi_SeriesB2TrancheLiabilityMember_documentation_en-US" xlink:label="lab_tlsi_SeriesB2TrancheLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B-2 Tranche Liability</link:label>
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    <link:label id="lab_tlsi_PreferredStockIssuedPricePerShare_297dd813-4da1-42d5-b46c-5a2a6d584e36_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Original issue price (in dollars per share)</link:label>
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    <link:label id="lab_tlsi_PreferredStockIssuedPricePerShare_documentation_en-US" xlink:label="lab_tlsi_PreferredStockIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Issued Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockIssuedPricePerShare" xlink:href="tlsi-20230930.xsd#tlsi_PreferredStockIssuedPricePerShare"/>
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    <link:label id="lab_us-gaap_EarningsPerShareDiluted_5ea16a00-b041-44f3-8eff-847ef5e2c426_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net loss per share, diluted (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightLineItems_3549e8bb-946a-4b37-a602-3ab46c96230a_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightLineItems" xlink:to="lab_us-gaap_ClassOfWarrantOrRightLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_3b996f0e-88f8-4f56-b0fb-f17044e6c7bb_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_us-gaap_AccountsReceivableNetCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsReceivableNetCurrent" xlink:to="lab_us-gaap_AccountsReceivableNetCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized_949d5de4-52e7-4def-a149-35b9593ba6b7_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum shares of common stock allowed under Purchase Agreement (in shares)</link:label>
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    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized_documentation_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Standby Equity Purchase Agreement, Maximum Amount Of Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:href="tlsi-20230930.xsd#tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:to="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SeriesA4ConvertiblePreferredStockMember_89301459-1711-476c-97a2-c4bbe56763fa_terseLabel_en-US" xlink:label="lab_tlsi_SeriesA4ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-4</link:label>
    <link:label id="lab_tlsi_SeriesA4ConvertiblePreferredStockMember_label_en-US" xlink:label="lab_tlsi_SeriesA4ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-4 Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_tlsi_SeriesA4ConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_tlsi_SeriesA4ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-4 Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SeriesA4ConvertiblePreferredStockMember" xlink:href="tlsi-20230930.xsd#tlsi_SeriesA4ConvertiblePreferredStockMember"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_79bfd3ae-6e49-4977-9bfe-cefd60851430_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise of options</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock Issued During Period, Value, Stock Options Exercised</link:label>
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    <link:label id="lab_dei_TradingSymbol_d1f89aed-91d5-49d1-9eed-509e03c3e962_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_TradingSymbol"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_961cf8fa-49a6-4aba-847f-75db6aacb101_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Options, weighted average fair value (in dollars per share)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
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    <link:label id="lab_us-gaap_NetIncomeLoss_5c652336-5478-4992-a7b4-28623785cb79_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net loss available to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_370a1f4e-461a-47f3-aee6-a1d67207e623_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_f88be8cf-5a47-4327-9970-1497b7b9127b_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net loss available to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Income (Loss)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_12827afb-3f95-49f0-b2c5-62e6eeee2478_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total current liabilities</link:label>
    <link:label id="lab_us-gaap_LiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesCurrent" xlink:to="lab_us-gaap_LiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
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    <link:label id="lab_tlsi_SeriesA5ConvertiblePreferredStockMember_8832d4b9-9c0f-4040-8295-008c90af662f_terseLabel_en-US" xlink:label="lab_tlsi_SeriesA5ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-5</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_38e989d7-6298-4855-8992-fbd45f72988e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Cash and Cash Equivalents</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_47b02ec7-456e-436e-8f4f-e11491434268_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities and Stockholders&#8217; Equity (Deficit)</link:label>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_4070ef9e-d891-491b-8535-51444438b4e1_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table]</link:label>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_f51cf045-1d91-45e2-9bbc-5d2c41cf1ee2_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise of options (in shares)</link:label>
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    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_6ef773d8-071c-4f35-883e-3256bf05c837_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cost of goods sold</link:label>
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    <link:label id="lab_tlsi_PreferredStockConversionPercentageOfOutstandingShares_e6bb113d-507f-4b5a-850e-7623f530514f_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockConversionPercentageOfOutstandingShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of then-outstanding preferred stock on an as-converted to common stock basis</link:label>
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    <link:label id="lab_tlsi_PreferredStockConversionPercentageOfOutstandingShares_documentation_en-US" xlink:label="lab_tlsi_PreferredStockConversionPercentageOfOutstandingShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Conversion, Percentage of Outstanding Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockConversionPercentageOfOutstandingShares" xlink:href="tlsi-20230930.xsd#tlsi_PreferredStockConversionPercentageOfOutstandingShares"/>
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    <link:label id="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock_ddf9ccc6-5072-4546-9bf5-654527ef9339_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Plan Balances</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockConversionPriceFloor" xlink:href="tlsi-20230930.xsd#tlsi_PreferredStockConversionPriceFloor"/>
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    <link:label id="lab_tlsi_DerivativeInstrumentPeriodTwoMember_eb0916ac-d49f-4ecd-b969-538469d70da4_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche Two</link:label>
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    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_9824d7d2-258d-4bf1-bbbd-d240811d7379_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Summary of Significant Accounting Policies</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_227ff342-12ea-48f0-b4f0-8c3cb3672b6a_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Inputs, Level 1</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SeriesA3ConvertiblePreferredStockMember_fc0a3b77-143b-495d-a698-a05da4663b85_terseLabel_en-US" xlink:label="lab_tlsi_SeriesA3ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-3</link:label>
    <link:label id="lab_tlsi_SeriesA3ConvertiblePreferredStockMember_label_en-US" xlink:label="lab_tlsi_SeriesA3ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-3 Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_tlsi_SeriesA3ConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_tlsi_SeriesA3ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-3 Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SeriesA3ConvertiblePreferredStockMember" xlink:href="tlsi-20230930.xsd#tlsi_SeriesA3ConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SeriesA3ConvertiblePreferredStockMember" xlink:to="lab_tlsi_SeriesA3ConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_e59cf996-d13a-453c-bf4b-0ddd0e738cb1_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_c3429a64-06ee-4d4d-84be-5a105333d24a_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercise price of warrants (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right, Exercise Price of Warrants or Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:to="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_52dc61ca-c5e9-422e-bd38-0283feb908a7_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Available for Issue (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionDomain_12b9ef17-337e-48a6-bc9a-6ba004822464_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionDomain_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetAcquisitionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionDomain" xlink:to="lab_us-gaap_AssetAcquisitionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_2805d58a-d084-407c-add3-35890be88bf9_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Options granted (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntitySmallBusiness_cc01149f-96de-4e21-8889-39ad272eb21c_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Small Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntitySmallBusiness" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntitySmallBusiness"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntitySmallBusiness" xlink:to="lab_dei_EntitySmallBusiness" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_8806ccb1-a498-4669-a23c-c7173814dfd8_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_LocalPhoneNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LocalPhoneNumber" xlink:to="lab_dei_LocalPhoneNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_2ad5f8b5-8bcf-4777-ab8d-78e63f0ef3fd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts receivable</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Accounts Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInAccountsReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements_bde8aaf2-cecb-4c4a-82c7-15c597a790ce_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Settlements</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Settlements</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_MedTechAcquisitionCorporationMember_25da0977-afec-4779-955b-2eb5f4921bbd_terseLabel_en-US" xlink:label="lab_tlsi_MedTechAcquisitionCorporationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">MedTech Acquisition Corporation</link:label>
    <link:label id="lab_tlsi_MedTechAcquisitionCorporationMember_label_en-US" xlink:label="lab_tlsi_MedTechAcquisitionCorporationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">MedTech Acquisition Corporation [Member]</link:label>
    <link:label id="lab_tlsi_MedTechAcquisitionCorporationMember_documentation_en-US" xlink:label="lab_tlsi_MedTechAcquisitionCorporationMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">MedTech Acquisition Corporation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_MedTechAcquisitionCorporationMember" xlink:href="tlsi-20230930.xsd#tlsi_MedTechAcquisitionCorporationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_MedTechAcquisitionCorporationMember" xlink:to="lab_tlsi_MedTechAcquisitionCorporationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts_dd5be143-1df1-4179-a3b2-f1f5ab5a04ed_negatedTerseLabel_en-US" xlink:label="lab_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Offering costs related to Business Combination</link:label>
    <link:label id="lab_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts_ccc1371c-ef56-4905-803c-7162b031d621_verboseLabel_en-US" xlink:label="lab_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expenses related to business combination</link:label>
    <link:label id="lab_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts_label_en-US" xlink:label="lab_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments Of Reverse Recapitalization, Transaction Costs</link:label>
    <link:label id="lab_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts_documentation_en-US" xlink:label="lab_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments Of Reverse Recapitalization, Transaction Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:href="tlsi-20230930.xsd#tlsi_PaymentsOfReverseRecapitalizationTransactionCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:to="lab_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WarrantMember_e161b000-8d5f-491f-83ed-d7eee015dfb4_terseLabel_en-US" xlink:label="lab_us-gaap_WarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrants</link:label>
    <link:label id="lab_us-gaap_WarrantMember_label_en-US" xlink:label="lab_us-gaap_WarrantMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrant [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WarrantMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantMember" xlink:to="lab_us-gaap_WarrantMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised_a35ced2c-f46c-48f7-94ef-62a3ec876495_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrants exercised (in shares)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised_bffe4b7e-b13a-4ca8-8c56-0fd9e38e9706_negatedTerseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exercises (in shares)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right, Warrants Exercised</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right, Warrants Exercised</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:href="tlsi-20230930.xsd#tlsi_ClassOfWarrantOrRightWarrantsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:to="lab_tlsi_ClassOfWarrantOrRightWarrantsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice_61485c3f-da6b-4211-b49f-b1667a63d126_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Threshold number of business days before sending notice of redemption to warrant holders</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class Of Warrant Or Right, Conversion Days Notice</link:label>
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    <link:label id="lab_tlsi_PrivateWarrantsMember_e83bf9b1-1631-4972-9d75-b2fa07c4467f_terseLabel_en-US" xlink:label="lab_tlsi_PrivateWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Private Placement Warrants</link:label>
    <link:label id="lab_tlsi_PrivateWarrantsMember_label_en-US" xlink:label="lab_tlsi_PrivateWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Private Warrants [Member]</link:label>
    <link:label id="lab_tlsi_PrivateWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_PrivateWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Private Warrants</link:label>
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    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_31fae10c-9236-4e23-8270-cd16a627ffe8_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted stock units</link:label>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted Stock Units (RSUs) [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RestrictedStockUnitsRSUMember"/>
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    <link:label id="lab_tlsi_NatureOfBusinessTable_422cdc37-cc1b-4942-ac1e-d613f1b0a093_terseLabel_en-US" xlink:label="lab_tlsi_NatureOfBusinessTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Nature of Business [Table]</link:label>
    <link:label id="lab_tlsi_NatureOfBusinessTable_label_en-US" xlink:label="lab_tlsi_NatureOfBusinessTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Nature of Business [Table]</link:label>
    <link:label id="lab_tlsi_NatureOfBusinessTable_documentation_en-US" xlink:label="lab_tlsi_NatureOfBusinessTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Nature of Business [Table]</link:label>
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    <link:label id="lab_us-gaap_ClassOfWarrantOrRightTable_928f7961-847a-49dc-a99f-5300e5721064_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right [Table]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightTable_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightTable" xlink:to="lab_us-gaap_ClassOfWarrantOrRightTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable_55875907-3a32-49df-9501-e5f8ad246244_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Table]</link:label>
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    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
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    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_50d4661e-bc4a-4907-877a-7c79bcf19514_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash, Cash Equivalents and Restricted Cash</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
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    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_c2b44c73-b90a-4cb4-9609-4991ec8909d8_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of stock (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:to="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PayablesAndAccrualsAbstract_label_en-US" xlink:label="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payables and Accruals [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PayablesAndAccrualsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PayablesAndAccrualsAbstract" xlink:to="lab_us-gaap_PayablesAndAccrualsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember_e3ede3cc-ad07-429f-b2ce-6422f8afde86_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Risk-free interest rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Input, Risk Free Interest Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputRiskFreeInterestRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:to="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_05d09ad0-b550-44bb-99b4-5d14af624f76_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value by Liability Class [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_7f0c09b4-f771-434a-999d-5255c3674b5a_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock"/>
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    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_7b01074b-f656-470e-bcff-838e698c1c87_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Convertible preferred stock</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_b5684fcb-88bc-427d-91ea-d447004a6642_periodStartLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Convertible preferred stock, beginning balance</link:label>
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    <link:label id="lab_tlsi_ContingentEarnoutLiabilityMember_06c5350e-cd2d-49f6-8b78-c98328cf4c22_terseLabel_en-US" xlink:label="lab_tlsi_ContingentEarnoutLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contingent earnout liability</link:label>
    <link:label id="lab_tlsi_ContingentEarnoutLiabilityMember_label_en-US" xlink:label="lab_tlsi_ContingentEarnoutLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contingent Earnout Liability [Member]</link:label>
    <link:label id="lab_tlsi_ContingentEarnoutLiabilityMember_documentation_en-US" xlink:label="lab_tlsi_ContingentEarnoutLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contingent Earnout Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ContingentEarnoutLiabilityMember" xlink:href="tlsi-20230930.xsd#tlsi_ContingentEarnoutLiabilityMember"/>
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    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays_2fa1b389-1afe-4268-8ab2-beaceddfc65e_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of warrant or right, conversion terms, threshold consecutive trading days</link:label>
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    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_26ea2807-72d0-4b59-8b40-a0d17314adb8_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Recent Accounting Pronouncements</link:label>
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    <link:label id="lab_us-gaap_SaleOfStockPricePerShare_4ce60dcd-87d9-48e2-946a-76e83b290672_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of stock, price per share (in dollars per share)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockPricePerShare" xlink:to="lab_us-gaap_SaleOfStockPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_d39664d3-300d-491b-961a-6a3dcec9c86a_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Interest income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterest_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investment Income, Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InvestmentIncomeInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterest" xlink:to="lab_us-gaap_InvestmentIncomeInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount_bdd1eebc-b667-465e-8e98-2c71e00ee12f_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Royalties as a percentage of net sales, under sales threshold</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Royalty Percentage, Under Threshold Amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Royalty Percentage, Under Threshold Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:href="tlsi-20230930.xsd#tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:to="lab_tlsi_AssetAcquisitionRoyaltyPercentageUnderThresholdAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_ba6dcf69-d9b6-4a3a-8348-a8f1ba2f28e6_terseLabel_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Impairment and Disposal of Long-Lived Assets</link:label>
    <link:label id="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Impairment or Disposal of Long-Lived Assets, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:to="lab_us-gaap_ImpairmentOrDisposalOfLongLivedAssetsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_004a8a77-a01f-46f8-9432-3fe1231b5a58_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GrossProfit_c40567a0-2942-494e-934c-7a7dd38e0642_totalLabel_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gross profit</link:label>
    <link:label id="lab_us-gaap_GrossProfit_label_en-US" xlink:label="lab_us-gaap_GrossProfit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gross Profit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GrossProfit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GrossProfit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GrossProfit" xlink:to="lab_us-gaap_GrossProfit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare_e921c33a-5a63-4be6-a499-b7f192eb0f75_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Convertible preferred stock, par value per share (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Temporary Equity, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:to="lab_us-gaap_TemporaryEquityParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_62e1ba89-c1d5-4877-a1b9-ad5d6350ff47_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_532bdd6e-db08-4457-96c5-4678a6e7a4d8_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Payment Arrangement [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_39f35ad2-fb10-4825-8b55-24268bd71c3a_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net proceeds on sale of stock</link:label>
    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SaleOfStockConsiderationReceivedOnTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:to="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_BinomialTrancheModelMember_b6aa19ac-eed2-46b8-9f0c-7db447a594e4_terseLabel_en-US" xlink:label="lab_tlsi_BinomialTrancheModelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Binomial Tranche Model</link:label>
    <link:label id="lab_tlsi_BinomialTrancheModelMember_label_en-US" xlink:label="lab_tlsi_BinomialTrancheModelMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Binomial Tranche Model [Member]</link:label>
    <link:label id="lab_tlsi_BinomialTrancheModelMember_documentation_en-US" xlink:label="lab_tlsi_BinomialTrancheModelMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Binomial Tranche Model</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_BinomialTrancheModelMember" xlink:href="tlsi-20230930.xsd#tlsi_BinomialTrancheModelMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_BinomialTrancheModelMember" xlink:to="lab_tlsi_BinomialTrancheModelMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_6fe86ada-52db-45c0-afa9-4ddec727a4c2_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Options to purchase common stock</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Employee Stock Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_4ebf79d0-58b8-4f68-ba93-39a2c820fa37_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contingent Earnout Liability</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instruments and Hedging Activities Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:to="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SeriesB2ConvertiblePreferredStockMember_704a286a-c550-4b8d-8803-adf6e30a4e04_terseLabel_en-US" xlink:label="lab_tlsi_SeriesB2ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B-2</link:label>
    <link:label id="lab_tlsi_SeriesB2ConvertiblePreferredStockMember_label_en-US" xlink:label="lab_tlsi_SeriesB2ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B-2 Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_tlsi_SeriesB2ConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_tlsi_SeriesB2ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B-2 Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SeriesB2ConvertiblePreferredStockMember" xlink:href="tlsi-20230930.xsd#tlsi_SeriesB2ConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SeriesB2ConvertiblePreferredStockMember" xlink:to="lab_tlsi_SeriesB2ConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionTable_8e9ba9a9-e7b1-48ec-820a-91bed4c83bd1_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition [Table]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionTable" xlink:to="lab_us-gaap_AssetAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_29bc5af5-dfb7-4904-a944-3ed41bfcf1e4_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentType_864ab852-fb20-439d-8344-a0ab77481f56_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentType" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentType"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentType" xlink:to="lab_dei_DocumentType" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember_201252ee-7c7d-4493-96e5-fe69d6bf6c15_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrant liability</link:label>
    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember_label_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Financial Instruments, Warrant Liability [Member]</link:label>
    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember_documentation_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Financial Instruments, Warrant Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember" xlink:to="lab_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_982c9840-dee4-40c7-94de-04465690f8f0_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryPolicyTextBlock_a55ae264-4340-455a-ac30-35a9f8a63243_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory</link:label>
    <link:label id="lab_us-gaap_InventoryPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_InventoryPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryPolicyTextBlock" xlink:to="lab_us-gaap_InventoryPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_RecapitalizationExchangeRatio_116a17ba-0530-43b4-a007-f505bf339b54_terseLabel_en-US" xlink:label="lab_tlsi_RecapitalizationExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Exchange ratio</link:label>
    <link:label id="lab_tlsi_RecapitalizationExchangeRatio_label_en-US" xlink:label="lab_tlsi_RecapitalizationExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Recapitalization Exchange Ratio</link:label>
    <link:label id="lab_tlsi_RecapitalizationExchangeRatio_documentation_en-US" xlink:label="lab_tlsi_RecapitalizationExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Recapitalization Exchange Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RecapitalizationExchangeRatio" xlink:href="tlsi-20230930.xsd#tlsi_RecapitalizationExchangeRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_RecapitalizationExchangeRatio" xlink:to="lab_tlsi_RecapitalizationExchangeRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionTextBlock_fc6be9dd-2a20-40c9-a896-db9093564de3_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dynavax Purchase</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionTextBlock_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetAcquisitionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionTextBlock" xlink:to="lab_us-gaap_AssetAcquisitionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_89052752-48ea-4a81-8b97-5693496fcebe_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesNameDomain_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Antidilutive Securities, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AntidilutiveSecuritiesNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:to="lab_us-gaap_AntidilutiveSecuritiesNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesCurrent_81d13f39-29ba-4960-a202-32c605a0eb62_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative liability, current</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesCurrent" xlink:to="lab_us-gaap_DerivativeLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_7c7cd75a-11d0-473c-80d4-5ca112dd870c_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation</link:label>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Payment Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromContributedCapital_e9a7b39d-036d-44b2-a128-13a5f8f8755f_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromContributedCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from MTAC trust account</link:label>
    <link:label id="lab_us-gaap_ProceedsFromContributedCapital_label_en-US" xlink:label="lab_us-gaap_ProceedsFromContributedCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Contributed Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromContributedCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromContributedCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromContributedCapital" xlink:to="lab_us-gaap_ProceedsFromContributedCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_488b0423-4f3c-474d-adab-38d00e91a002_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputSharePriceMember_c5098062-8397-4f69-b0fe-19051e3bdbfe_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current stock price</link:label>
    <link:label id="lab_us-gaap_MeasurementInputSharePriceMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Input, Share Price [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputSharePriceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputSharePriceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputSharePriceMember" xlink:to="lab_us-gaap_MeasurementInputSharePriceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable_a8012708-3206-4f23-8832-77b86c716b71_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityTransfersNet_f2a3c309-a471-4637-a7a5-2bd5bd64f00e_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityTransfersNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Transfer In (Out) of Level&#160;3</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityTransfersNet_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityTransfersNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Transfers, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityTransfersNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityTransfersNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityTransfersNet" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityTransfersNet" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_NumberOfProductLinesInDevelopment_bed00c50-ed72-401e-9f6c-b03f72e647ba_terseLabel_en-US" xlink:label="lab_tlsi_NumberOfProductLinesInDevelopment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of product lines in development</link:label>
    <link:label id="lab_tlsi_NumberOfProductLinesInDevelopment_label_en-US" xlink:label="lab_tlsi_NumberOfProductLinesInDevelopment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of Product Lines in Development</link:label>
    <link:label id="lab_tlsi_NumberOfProductLinesInDevelopment_documentation_en-US" xlink:label="lab_tlsi_NumberOfProductLinesInDevelopment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of Product Lines in Development</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_NumberOfProductLinesInDevelopment" xlink:href="tlsi-20230930.xsd#tlsi_NumberOfProductLinesInDevelopment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_NumberOfProductLinesInDevelopment" xlink:to="lab_tlsi_NumberOfProductLinesInDevelopment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventMember_a44679aa-e2d7-4458-946a-8a135b64abc7_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event</link:label>
    <link:label id="lab_us-gaap_SubsequentEventMember_label_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventMember" xlink:to="lab_us-gaap_SubsequentEventMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashNoncurrent_eb473c88-8592-4c12-90cf-98e9a3d22d27_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted cash (included in Other assets)</link:label>
    <link:label id="lab_us-gaap_RestrictedCashNoncurrent_label_en-US" xlink:label="lab_us-gaap_RestrictedCashNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restricted Cash, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RestrictedCashNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashNoncurrent" xlink:to="lab_us-gaap_RestrictedCashNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_6926a254-6a03-4dc9-9cf7-19d57f02ff9c_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other current liabilities</link:label>
    <link:label id="lab_us-gaap_OtherLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockConvertibleConversionRatio_531fe22c-5ae4-4011-900b-497c40da0f25_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockConvertibleConversionRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Conversion ratio</link:label>
    <link:label id="lab_us-gaap_PreferredStockConvertibleConversionRatio_label_en-US" xlink:label="lab_us-gaap_PreferredStockConvertibleConversionRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Convertible, Conversion Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockConvertibleConversionRatio" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockConvertibleConversionRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockConvertibleConversionRatio" xlink:to="lab_us-gaap_PreferredStockConvertibleConversionRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_bf7c8292-843c-4b10-9733-2a638e605a6a_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Trade payables, accrued expenses and other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Accounts Payable and Accrued Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeStatementAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementAbstract" xlink:to="lab_us-gaap_IncomeStatementAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryRawMaterialsNetOfReserves_67bae695-1496-4f4a-8518-d2828150099d_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryRawMaterialsNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Raw materials</link:label>
    <link:label id="lab_us-gaap_InventoryRawMaterialsNetOfReserves_label_en-US" xlink:label="lab_us-gaap_InventoryRawMaterialsNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory, Raw Materials, Net of Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryRawMaterialsNetOfReserves" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryRawMaterialsNetOfReserves"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryRawMaterialsNetOfReserves" xlink:to="lab_us-gaap_InventoryRawMaterialsNetOfReserves" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ReverseRecapitalizationLineItems_3df38e2f-8892-402b-8aa9-89880f898991_terseLabel_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization [Line Items]</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationLineItems_label_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization [Line Items]</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationLineItems_documentation_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationLineItems" xlink:href="tlsi-20230930.xsd#tlsi_ReverseRecapitalizationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ReverseRecapitalizationLineItems" xlink:to="lab_tlsi_ReverseRecapitalizationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_TrancheDomain_3ab96371-76e4-426c-9bd0-fb4a2416dd67_terseLabel_en-US" xlink:label="lab_tlsi_TrancheDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche [Domain]</link:label>
    <link:label id="lab_tlsi_TrancheDomain_label_en-US" xlink:label="lab_tlsi_TrancheDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche [Domain]</link:label>
    <link:label id="lab_tlsi_TrancheDomain_documentation_en-US" xlink:label="lab_tlsi_TrancheDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_TrancheDomain" xlink:href="tlsi-20230930.xsd#tlsi_TrancheDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_TrancheDomain" xlink:to="lab_tlsi_TrancheDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_d919e8f6-f369-4fe4-8eb0-29ba0559a523_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Issuance of preferred stock with PIPE financing (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_49344d35-ec8d-4a2c-bd32-a95316adca89_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Issuances (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock Issued During Period, Shares, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodSharesNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_87076783-7dea-427c-b114-7ac749d094c5_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_55e41512-e915-4c2c-a35c-3eda9b6b0e01_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays_89e129a0-cc49-4429-b13f-ca5a3db5db21_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnout period, threshold trading days</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Threshold Trading Days</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Threshold Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:to="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WarrantsAndRightsNoteDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsNoteDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrants and Rights Note Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantsAndRightsNoteDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WarrantsAndRightsNoteDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantsAndRightsNoteDisclosureAbstract" xlink:to="lab_us-gaap_WarrantsAndRightsNoteDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears_3db0e782-13bb-4530-acf5-527b860c7146_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share reserve increase, number of years</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Automatic Increase Per Year, Number of Years</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Automatic Increase Per Year, Number of Years</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:href="tlsi-20230930.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionLineItems_691d8fb0-8406-4a1b-9a47-dfd76a77219a_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition [Line Items]</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetAcquisitionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionLineItems" xlink:to="lab_us-gaap_AssetAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_36d377a2-863e-4304-b9b3-51bfa1aacd5b_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of warrant or right, number of securities called by each warrant or right (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right, Number of Securities Called by Each Warrant or Right</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:to="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilities_a319f5da-1d9b-407e-94bd-bcadec27298d_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Outstanding warrant liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockConvertibleDownRoundFeatureIncreaseDecreaseInEquityAmount1_c4bc34e6-c6ee-4724-abbc-ecb257d6f539_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockConvertibleDownRoundFeatureIncreaseDecreaseInEquityAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Deemed dividend</link:label>
    <link:label id="lab_us-gaap_PreferredStockConvertibleDownRoundFeatureIncreaseDecreaseInEquityAmount1_label_en-US" xlink:label="lab_us-gaap_PreferredStockConvertibleDownRoundFeatureIncreaseDecreaseInEquityAmount1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Convertible, Down Round Feature, Increase (Decrease) in Equity, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockConvertibleDownRoundFeatureIncreaseDecreaseInEquityAmount1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockConvertibleDownRoundFeatureIncreaseDecreaseInEquityAmount1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockConvertibleDownRoundFeatureIncreaseDecreaseInEquityAmount1" xlink:to="lab_us-gaap_PreferredStockConvertibleDownRoundFeatureIncreaseDecreaseInEquityAmount1" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount_7d061d7e-b03c-40bf-b5b4-2026a34843bf_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Royalties as a percentage of sales, over threshold amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Royalty Percentage, Over Threshold Amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Royalty Percentage, Over Threshold Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:href="tlsi-20230930.xsd#tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:to="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockAutomaticConversionPeriod_b2abedce-e4be-40cc-9d58-f01eff5cbf97_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockAutomaticConversionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Automatic conversion, anniversary</link:label>
    <link:label id="lab_tlsi_PreferredStockAutomaticConversionPeriod_label_en-US" xlink:label="lab_tlsi_PreferredStockAutomaticConversionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Automatic Conversion, Period</link:label>
    <link:label id="lab_tlsi_PreferredStockAutomaticConversionPeriod_documentation_en-US" xlink:label="lab_tlsi_PreferredStockAutomaticConversionPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Automatic Conversion, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockAutomaticConversionPeriod" xlink:href="tlsi-20230930.xsd#tlsi_PreferredStockAutomaticConversionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockAutomaticConversionPeriod" xlink:to="lab_tlsi_PreferredStockAutomaticConversionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:to="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SaleOfStockConsiderationReceivedOnTransactionPotentialIncreasedAmount_318e687c-e374-4204-a5a5-ca987ad0d921_terseLabel_en-US" xlink:label="lab_tlsi_SaleOfStockConsiderationReceivedOnTransactionPotentialIncreasedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Consideration received, potential increased amount</link:label>
    <link:label id="lab_tlsi_SaleOfStockConsiderationReceivedOnTransactionPotentialIncreasedAmount_label_en-US" xlink:label="lab_tlsi_SaleOfStockConsiderationReceivedOnTransactionPotentialIncreasedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction, Potential Increased Amount</link:label>
    <link:label id="lab_tlsi_SaleOfStockConsiderationReceivedOnTransactionPotentialIncreasedAmount_documentation_en-US" xlink:label="lab_tlsi_SaleOfStockConsiderationReceivedOnTransactionPotentialIncreasedAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock, Consideration Received on Transaction, Potential Increased Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SaleOfStockConsiderationReceivedOnTransactionPotentialIncreasedAmount" xlink:href="tlsi-20230930.xsd#tlsi_SaleOfStockConsiderationReceivedOnTransactionPotentialIncreasedAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SaleOfStockConsiderationReceivedOnTransactionPotentialIncreasedAmount" xlink:to="lab_tlsi_SaleOfStockConsiderationReceivedOnTransactionPotentialIncreasedAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Payment Arrangement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:to="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StockIssuedDuringPeriodSharesReverseRecapitalization_ebadcca8-b007-43e6-bb3f-3ff629dc770e_verboseLabel_en-US" xlink:label="lab_tlsi_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Issuance of common stock upon closing of the Business Combination (in shares)</link:label>
    <link:label id="lab_tlsi_StockIssuedDuringPeriodSharesReverseRecapitalization_label_en-US" xlink:label="lab_tlsi_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock Issued During Period, Shares, Reverse Recapitalization</link:label>
    <link:label id="lab_tlsi_StockIssuedDuringPeriodSharesReverseRecapitalization_documentation_en-US" xlink:label="lab_tlsi_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock Issued During Period, Shares, Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:href="tlsi-20230930.xsd#tlsi_StockIssuedDuringPeriodSharesReverseRecapitalization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:to="lab_tlsi_StockIssuedDuringPeriodSharesReverseRecapitalization" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_5e56bace-983f-478a-8b63-12cb57b6a96d_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount_1c713acc-280d-4af3-b86a-a61eb0f12586_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Maximum aggregate milestone payments per development milestone</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Maximum Milestone Amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Maximum Milestone Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:href="tlsi-20230930.xsd#tlsi_AssetAcquisitionMaximumMilestoneAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:to="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AdjustmentsToAdditionalPaidInCapitalWarrantsAssumedInReverseRecapitalization_1b81ef47-fa22-477c-9524-fc647dd95302_negatedTerseLabel_en-US" xlink:label="lab_tlsi_AdjustmentsToAdditionalPaidInCapitalWarrantsAssumedInReverseRecapitalization" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assumption of warrants to purchase common stock in connection with the Business Combination</link:label>
    <link:label id="lab_tlsi_AdjustmentsToAdditionalPaidInCapitalWarrantsAssumedInReverseRecapitalization_label_en-US" xlink:label="lab_tlsi_AdjustmentsToAdditionalPaidInCapitalWarrantsAssumedInReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Adjustments to Additional Paid in Capital, Warrants Assumed In Reverse Recapitalization</link:label>
    <link:label id="lab_tlsi_AdjustmentsToAdditionalPaidInCapitalWarrantsAssumedInReverseRecapitalization_documentation_en-US" xlink:label="lab_tlsi_AdjustmentsToAdditionalPaidInCapitalWarrantsAssumedInReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Adjustments to Additional Paid in Capital, Warrants Assumed In Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AdjustmentsToAdditionalPaidInCapitalWarrantsAssumedInReverseRecapitalization" xlink:href="tlsi-20230930.xsd#tlsi_AdjustmentsToAdditionalPaidInCapitalWarrantsAssumedInReverseRecapitalization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AdjustmentsToAdditionalPaidInCapitalWarrantsAssumedInReverseRecapitalization" xlink:to="lab_tlsi_AdjustmentsToAdditionalPaidInCapitalWarrantsAssumedInReverseRecapitalization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryNet_2b2da452-6716-480e-b511-d963421d1091_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory, net</link:label>
    <link:label id="lab_us-gaap_InventoryNet_af38f5ea-03ff-47bc-a3c2-aaf8d092b87f_totalLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory, net</link:label>
    <link:label id="lab_us-gaap_InventoryNet_label_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryNet" xlink:to="lab_us-gaap_InventoryNet" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightDaysFromWhichWarrantOrRightsBecomeExercisable_8080792e-c0e4-445f-b8d1-83e6e166a9c6_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightDaysFromWhichWarrantOrRightsBecomeExercisable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrant exercise period</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightDaysFromWhichWarrantOrRightsBecomeExercisable_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightDaysFromWhichWarrantOrRightsBecomeExercisable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class Of Warrant Or Right, Days From Which Warrant Or Rights Become Exercisable</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightDaysFromWhichWarrantOrRightsBecomeExercisable_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightDaysFromWhichWarrantOrRightsBecomeExercisable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class Of Warrant Or Right, Days From Which Warrant Or Rights Become Exercisable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightDaysFromWhichWarrantOrRightsBecomeExercisable" xlink:href="tlsi-20230930.xsd#tlsi_ClassOfWarrantOrRightDaysFromWhichWarrantOrRightsBecomeExercisable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightDaysFromWhichWarrantOrRightsBecomeExercisable" xlink:to="lab_tlsi_ClassOfWarrantOrRightDaysFromWhichWarrantOrRightsBecomeExercisable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfPrivatePlacement_17332a25-fe16-4183-bc67-de9a60be145c_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from private placement</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfPrivatePlacement_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Issuance of Private Placement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfPrivatePlacement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_9eedb923-910b-4f13-b53f-e5d4e6336e0c_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_808e4b97-06b1-4de2-bf8b-e88475d7868d_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_BlackScholesModelMember_e38db589-367a-43ee-9c3b-a698329357bd_terseLabel_en-US" xlink:label="lab_tlsi_BlackScholesModelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Black-Scholes Model</link:label>
    <link:label id="lab_tlsi_BlackScholesModelMember_label_en-US" xlink:label="lab_tlsi_BlackScholesModelMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Black-Scholes Model [Member]</link:label>
    <link:label id="lab_tlsi_BlackScholesModelMember_documentation_en-US" xlink:label="lab_tlsi_BlackScholesModelMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Black-Scholes Model</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_BlackScholesModelMember" xlink:href="tlsi-20230930.xsd#tlsi_BlackScholesModelMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_BlackScholesModelMember" xlink:to="lab_tlsi_BlackScholesModelMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_76592169-9c25-4aa7-96d4-a26e0e1f24ab_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_f540076d-0dd0-4ac5-9e2f-3b0314bb06cd_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Supplemental disclosure of noncash items:</link:label>
    <link:label id="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash Flow, Noncash Investing and Financing Activities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:to="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_InventoryDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryDisclosureAbstract" xlink:to="lab_us-gaap_InventoryDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_b6d01b7e-1068-408a-86a2-15d8ea6cea8d_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance_ca16f371-3cd9-4595-b5b6-2233ff36848a_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock available for future issuance (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance_label_en-US" xlink:label="lab_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Capital Shares Reserved for Future Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance" xlink:to="lab_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_16c209d4-075c-4b10-b026-4be71dd21159_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_6572398e-932f-4906-bdbc-e0fd885c525f_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_f5f847b6-17fb-415d-bcdb-a62be4d1b6c9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_ce98391f-2f7f-4331-b17c-468c68339e53_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue Recognition</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RevenueFromContractWithCustomerPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightStrikePriceOfWarrantsOrRights_fecf1a8c-e2c2-465f-9636-7694a042ac50_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightStrikePriceOfWarrantsOrRights" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Strike price (in dollars per share)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightStrikePriceOfWarrantsOrRights_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightStrikePriceOfWarrantsOrRights" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right, Strike Price of Warrants or Rights</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightStrikePriceOfWarrantsOrRights_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightStrikePriceOfWarrantsOrRights" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right, Strike Price of Warrants or Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightStrikePriceOfWarrantsOrRights" xlink:href="tlsi-20230930.xsd#tlsi_ClassOfWarrantOrRightStrikePriceOfWarrantsOrRights"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightStrikePriceOfWarrantsOrRights" xlink:to="lab_tlsi_ClassOfWarrantOrRightStrikePriceOfWarrantsOrRights" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_e5fb8b5c-5d5a-44d1-9561-b3fe371442c4_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:label id="lab_dei_EntityIncorporationStateCountryCode_label_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityIncorporationStateCountryCode" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityIncorporationStateCountryCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityIncorporationStateCountryCode" xlink:to="lab_dei_EntityIncorporationStateCountryCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_22f7f1a0-7597-47f6-a3a9-9fc6d8775468_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current assets:</link:label>
    <link:label id="lab_us-gaap_AssetsCurrentAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets, Current [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrentAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsCurrentAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrentAbstract" xlink:to="lab_us-gaap_AssetsCurrentAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DynavaxTechnologiesMember_75f333bc-f88e-43f1-b21d-becc2f60dabd_terseLabel_en-US" xlink:label="lab_tlsi_DynavaxTechnologiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dynavax Technologies</link:label>
    <link:label id="lab_tlsi_DynavaxTechnologiesMember_label_en-US" xlink:label="lab_tlsi_DynavaxTechnologiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dynavax Technologies [Member]</link:label>
    <link:label id="lab_tlsi_DynavaxTechnologiesMember_documentation_en-US" xlink:label="lab_tlsi_DynavaxTechnologiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Dynavax Technologies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DynavaxTechnologiesMember" xlink:href="tlsi-20230930.xsd#tlsi_DynavaxTechnologiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DynavaxTechnologiesMember" xlink:to="lab_tlsi_DynavaxTechnologiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressStateOrProvince_0648b688-534f-4a6a-a2ab-1e23e6f831e3_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:label id="lab_dei_EntityAddressStateOrProvince_label_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, State or Province</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressStateOrProvince" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressStateOrProvince"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressStateOrProvince" xlink:to="lab_dei_EntityAddressStateOrProvince" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CounterpartyNameAxis_b6f6a496-e4cd-4fbd-b0f2-810bef1437b7_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:label id="lab_srt_CounterpartyNameAxis_label_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Counterparty Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CounterpartyNameAxis" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_CounterpartyNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CounterpartyNameAxis" xlink:to="lab_srt_CounterpartyNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PurchaseAgreementExchangeCap_29247101-9186-4e5f-bf4e-df34638b5ff7_terseLabel_en-US" xlink:label="lab_tlsi_PurchaseAgreementExchangeCap" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase agreement, exchange cap</link:label>
    <link:label id="lab_tlsi_PurchaseAgreementExchangeCap_label_en-US" xlink:label="lab_tlsi_PurchaseAgreementExchangeCap" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase Agreement, Exchange Cap</link:label>
    <link:label id="lab_tlsi_PurchaseAgreementExchangeCap_documentation_en-US" xlink:label="lab_tlsi_PurchaseAgreementExchangeCap" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase Agreement, Exchange Cap</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PurchaseAgreementExchangeCap" xlink:href="tlsi-20230930.xsd#tlsi_PurchaseAgreementExchangeCap"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PurchaseAgreementExchangeCap" xlink:to="lab_tlsi_PurchaseAgreementExchangeCap" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_a83dbc75-4e3a-4286-89ef-fb729a4a3964_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrant and Tranche Liabilities / Contingent Earnout Liability</link:label>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivatives, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativesPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativesPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativesPolicyTextBlock" xlink:to="lab_us-gaap_DerivativesPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_e05427b9-8195-46fa-b815-b2a99159874b_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_1a359090-8fc7-4193-888d-5c40c372c29e_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_8aa4f1fc-5f38-4418-9328-caef3b4e1737_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightDomain" xlink:to="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ReverseRecapitalizationTransactionCostsIncurred_e1fa6ed2-5488-4003-9930-752cc180afa7_terseLabel_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationTransactionCostsIncurred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Transaction costs incurred</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationTransactionCostsIncurred_label_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationTransactionCostsIncurred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization, Transaction Costs Incurred</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationTransactionCostsIncurred_documentation_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationTransactionCostsIncurred" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization, Transaction Costs Incurred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationTransactionCostsIncurred" xlink:href="tlsi-20230930.xsd#tlsi_ReverseRecapitalizationTransactionCostsIncurred"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ReverseRecapitalizationTransactionCostsIncurred" xlink:to="lab_tlsi_ReverseRecapitalizationTransactionCostsIncurred" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_ConcentrationRiskCreditRisk_1ea205ad-04ef-440f-8eda-b03eaab701aa_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskCreditRisk" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Concentration of Credit Risk and Other Risks and Uncertainties</link:label>
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    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_30083055-a890-4bbd-8fb4-377556735de6_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_e4bf8377-4d0f-42b8-b9cd-1e32dbbae144_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsidiarySaleOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsidiarySaleOfStockAxis"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_9806d64a-24ea-4c66-93c0-21fc34b38607_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash used in investing activities</link:label>
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    <link:label id="lab_us-gaap_ClassOfStockDomain_ee669847-206d-400e-83a9-2978d2bc4309_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockDomain_label_en-US" xlink:label="lab_us-gaap_ClassOfStockDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfStockDomain"/>
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    <link:label id="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock_f9b3da8b-5ced-4dbb-82c5-ae63b452d32e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInventoryCurrentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Summary of Components of Inventory</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_78287584-3218-455b-977c-a8e56e301ba6_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net loss attributable to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements_feda333e-304e-477a-9ca0-1344c6913d82_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Issuances (Settlements)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchasesSalesIssuancesSettlements"/>
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    <link:label id="lab_us-gaap_DerivativeLiabilitiesNoncurrent_529068d5-5c41-4a42-9d80-cbc3d7972e5b_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative liability, noncurrent</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:to="lab_us-gaap_DerivativeLiabilitiesNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations_79344297-f36a-4fb7-9b66-cfaf2b83160b_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Effective federal tax rate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EffectiveIncomeTaxRateContinuingOperations"/>
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    <link:label id="lab_us-gaap_PlanNameAxis_6be25131-fb55-49e5-918c-fe516c2b613e_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Plan Name [Axis]</link:label>
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    <link:label id="lab_us-gaap_NumberOfReportableSegments_1da2ae8a-bf94-48b9-8cb8-0cb53c840344_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of reportable segments</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardExercisePriceGrantedPercent_f51392dc-3268-4356-8324-339e2ba7ffe8_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardExercisePriceGrantedPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock options exercise price, percentage of fair value</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareAbstract_f1931341-5dc5-48a9-b950-231282b60a7f_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareAbstract"/>
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    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementTerm_a887bc52-50f9-42a6-9cdd-c457dd8569db_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase agreement period</link:label>
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    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementTerm_documentation_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Standby Equity Purchase Agreement, Term</link:label>
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    <link:label id="lab_us-gaap_SellingAndMarketingExpense_3451ddf3-1844-444c-a459-a09121e95f76_terseLabel_en-US" xlink:label="lab_us-gaap_SellingAndMarketingExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sales and marketing</link:label>
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    <link:label id="lab_us-gaap_CommonStockValue_06647c14-b5fe-4efe-a5ca-7f66471117a6_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock, $0.0001 par value per share. Authorized 400,000,000 and 30,898,162 shares at September&#160;30, 2023, and December&#160;31, 2022, respectively; issued and outstanding, 26,316,681 and 347,926 shares at September&#160;30, 2023, and December&#160;31, 2022, respectively</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock, Value, Issued</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityByClassOfStockTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityByClassOfStockTable"/>
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    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_5a652ebd-e05f-4fb1-b57e-146547fc6c66_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">General and administrative</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightNumberOfWarrantsRepurchased_b75c2447-d3fc-4b3b-a0c0-60437bf2f73a_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightNumberOfWarrantsRepurchased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrants repurchased (in shares)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightNumberOfWarrantsRepurchased" xlink:to="lab_tlsi_ClassOfWarrantOrRightNumberOfWarrantsRepurchased" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
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    <link:label id="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Segment Reporting, Policy [Policy Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_SegmentReportingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrent_71995f4e-918e-4824-9624-85c83dc5d3bd_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total current assets</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsCurrent" xlink:to="lab_us-gaap_AssetsCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockMember_dbe03d16-2a74-4582-962c-5945b34a983d_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockMember_label_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockMember" xlink:to="lab_us-gaap_PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_9901da30-d5ac-4ab9-837a-a3be46c209c2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments on finance lease liabilities</link:label>
    <link:label id="lab_us-gaap_FinanceLeasePrincipalPayments_label_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finance Lease, Principal Payments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FinanceLeasePrincipalPayments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinanceLeasePrincipalPayments" xlink:to="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_b075ba84-e56b-4f26-b0ff-763ca4a00017_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other expense, net</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Nonoperating Income (Expense)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherNonoperatingIncomeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpense" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_957da9e7-1da3-42f1-a064-b3d372223000_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset_08bd1297-ec6a-44b2-91eb-930a73c67dac_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Conversion price, second automatic reset</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset_label_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Conversion Price, Automatic Reset Duration, Second Reset</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset_documentation_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Conversion Price, Automatic Reset Duration, Second Reset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:href="tlsi-20230930.xsd#tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:to="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage_d70c3839-5b34-4f53-bbe7-5a7a5f9d32c5_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnout shares vesting percentage</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Vesting Percentage</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Vesting Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:to="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementTable_8333c3f8-720f-4f15-bbcc-5445e31da9b7_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementTable" xlink:to="lab_us-gaap_StatementTable" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_80f8789e-c959-473b-8d86-bb410b934a75_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CurrentFiscalYearEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CurrentFiscalYearEndDate" xlink:to="lab_dei_CurrentFiscalYearEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountsPayableTradeCurrent_2a95f1c7-45f9-4b69-85ff-3a1347417b07_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsPayableTradeCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Trade payables</link:label>
    <link:label id="lab_us-gaap_AccountsPayableTradeCurrent_label_en-US" xlink:label="lab_us-gaap_AccountsPayableTradeCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts Payable, Trade, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsPayableTradeCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountsPayableTradeCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountsPayableTradeCurrent" xlink:to="lab_us-gaap_AccountsPayableTradeCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExpectedDividendRateMember_6872c1ec-04a9-493d-8b48-471cd3ccf0e0_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Estimated dividend yield</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedDividendRateMember_90117504-517e-4723-9682-d37265388afd_verboseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Expected dividends</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedDividendRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Input, Expected Dividend Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputExpectedDividendRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:to="lab_us-gaap_MeasurementInputExpectedDividendRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_f13125f7-a6bd-403b-8fab-ab918e1a24a6_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_c0236ff0-3338-4c06-8bf7-d62bf0d7622c_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_75fb1d73-8e00-42ab-8703-5834e86f789c_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrants outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_18a1c359-1cbf-4e93-ba7f-e2662e7a02e1_periodStartLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrants outstanding, beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightOutstanding_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:to="lab_us-gaap_ClassOfWarrantOrRightOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_9e9691ed-8dce-4893-bae3-793914e5eb71_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesAuthorized" xlink:to="lab_us-gaap_PreferredStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock_f5214240-17a0-4b1d-8985-f6869a1cf7c2_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from the issuance of preferred stock</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfPreferredStockAndPreferenceStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_65a1fa8b-97bc-40a4-9c2a-8f94324aab90_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">RSU weighted average fair value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_82893dd5-8cc3-4a84-8ecd-b206b0cee645_periodStartLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_feb781d7-abf4-4978-a4d5-8e0f996e18b1_periodEndLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Ending balance (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_10d8dcf4-2bf3-43b0-a749-da77977ee7cd_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesOutstanding" xlink:to="lab_us-gaap_PreferredStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy_acc9454c-e318-42a5-b606-8762c2d67ccd_terseLabel_en-US" xlink:label="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts Receivable</link:label>
    <link:label id="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy_label_en-US" xlink:label="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounts Receivable [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TradeAndOtherAccountsReceivablePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:to="lab_us-gaap_TradeAndOtherAccountsReceivablePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_2ea97374-2164-43ad-a352-64c3c33af453_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash used in operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Cash Provided by (Used in) Operating Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
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    <link:label id="lab_us-gaap_StatementClassOfStockAxis_c0779b1d-7e83-4ee4-85fa-fe43f86f571e_terseLabel_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementClassOfStockAxis_label_en-US" xlink:label="lab_us-gaap_StatementClassOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Stock [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementClassOfStockAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementClassOfStockAxis"/>
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    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_dc560364-d21e-4849-bf47-dc92f9094688_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued liabilities</link:label>
    <link:label id="lab_us-gaap_OtherAccruedLiabilitiesCurrent_label_en-US" xlink:label="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Accrued Liabilities, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherAccruedLiabilitiesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:to="lab_us-gaap_OtherAccruedLiabilitiesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding_19b04673-d4e1-4d27-9c14-8a0c480e9970_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Outstanding (in shares)</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Outstanding</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:href="tlsi-20230930.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedSalariesCurrent_0095a2c5-3a96-418a-93be-36eb1305f03b_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedSalariesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued payroll</link:label>
    <link:label id="lab_us-gaap_AccruedSalariesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedSalariesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued Salaries, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedSalariesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccruedSalariesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedSalariesCurrent" xlink:to="lab_us-gaap_AccruedSalariesCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightTransferOfWarrantToPreferredStock_54386c98-bfd4-48ab-8fc0-df51b1fcb67c_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightTransferOfWarrantToPreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Transfer of warrant liability to preferred stock upon exercise of warrants</link:label>
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    <link:label id="lab_tlsi_ClassOfWarrantOrRightTransferOfWarrantToPreferredStock_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightTransferOfWarrantToPreferredStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right, Transfer of Warrant to Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightTransferOfWarrantToPreferredStock" xlink:href="tlsi-20230930.xsd#tlsi_ClassOfWarrantOrRightTransferOfWarrantToPreferredStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightTransferOfWarrantToPreferredStock" xlink:to="lab_tlsi_ClassOfWarrantOrRightTransferOfWarrantToPreferredStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NatureOfOperations_1261101b-3d0f-4712-b34b-39c0c3a30f55_terseLabel_en-US" xlink:label="lab_us-gaap_NatureOfOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Nature of Business</link:label>
    <link:label id="lab_us-gaap_NatureOfOperations_label_en-US" xlink:label="lab_us-gaap_NatureOfOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Nature of Operations [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NatureOfOperations" xlink:to="lab_us-gaap_NatureOfOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount_658f493f-7086-4370-aee3-84cef46e880b_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Royalties, sales threshold amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Royalties, Sales Threshold Amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Royalties, Sales Threshold Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:href="tlsi-20230930.xsd#tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:to="lab_tlsi_AssetAcquisitionRoyaltiesSalesThresholdAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInformationLineItems_e7595ca9-0be3-4852-8ace-2bec96017b2b_terseLabel_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:label id="lab_dei_EntityInformationLineItems_label_en-US" xlink:label="lab_dei_EntityInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInformationLineItems" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInformationLineItems" xlink:to="lab_dei_EntityInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromWarrantExercises_525252ba-4054-4326-bd9c-d55c84a64759_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromWarrantExercises" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from exercise of preferred stock warrants</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromWarrantExercises" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromWarrantExercises"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromWarrantExercises" xlink:to="lab_us-gaap_ProceedsFromWarrantExercises" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combination and Asset Acquisition [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:to="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_7ed9285f-4e03-41c9-913c-b82b161ca10f_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total stockholders&#8217; equity (deficit)</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_24a2a0f1-ecc6-4aa6-93e2-4997184484aa_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance, beginning of period</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_7682a1f5-323c-4964-888e-791e7b21ddc3_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Balance, end of period</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity, Attributable to Parent</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays_e1ee5a9d-b1cf-4a81-94a9-93d8a12c3c2d_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase agreement, number of trading days used for measurement of market price</link:label>
    <link:label id="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays_label_en-US" xlink:label="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock, Share Price, Market Price, Number Of Consecutive Trading Days</link:label>
    <link:label id="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays_documentation_en-US" xlink:label="lab_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock, Share Price, Market Price, Number Of Consecutive Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays" xlink:href="tlsi-20230930.xsd#tlsi_CommonStockSharePriceMarketPriceNumberOfConsecutiveTradingDays"/>
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    <link:label id="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable_13c1cadd-dd68-4a06-85a9-8da1fcaf5a4a_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of warrant or right, threshold number of days for warrants to be transferable</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right, Threshold Number of Days for Warrants to be Transferable</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right, Threshold Number of Days for Warrants to be Transferable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:href="tlsi-20230930.xsd#tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:to="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_66b71856-f787-4d11-b31e-1b0d9ae22ef1_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock, $0.0001 par value</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_78f6c0c8-0a1e-4494-abc3-eaae3933489a_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_5c965327-5361-4a91-a005-df82a61fb7b9_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from the issuance of preferred stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Issuance of Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_e95e293d-ee09-40cf-a76b-1b209f713da2_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_7be3b02c-1937-42cd-98d0-d8383668440c_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_8b6bf6ac-33a9-422a-93ee-15e1c60f005e_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Loss per Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_70c4a2a6-e9d3-4ad1-a484-a62ec2de17cd_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Summary of Changes in Fair Value of Outstanding Warrant and Tranche Liabilities</link:label>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_2ea2929a-a5b6-4f6a-af1c-b1cd820b4f61_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodFourMember_ff80f8df-ae0d-46d9-afd7-a8f3729861f6_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche Four</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodFourMember_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period Four [Member]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodFourMember_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodFourMember" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeInstrumentPeriodFourMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentPeriodFourMember" xlink:to="lab_tlsi_DerivativeInstrumentPeriodFourMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedVacationCurrent_310269c9-75fd-4748-8146-1186cac8a8c9_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedVacationCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued vacation</link:label>
    <link:label id="lab_us-gaap_AccruedVacationCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedVacationCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accrued Vacation, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedVacationCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccruedVacationCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedVacationCurrent" xlink:to="lab_us-gaap_AccruedVacationCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MinimumMember_5827c282-b664-4313-a8f6-047cb24420c3_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Minimum</link:label>
    <link:label id="lab_srt_MinimumMember_label_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Minimum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MinimumMember" xlink:href="https://xbrl.fasb.org/srt/2023/elts/srt-2023.xsd#srt_MinimumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MinimumMember" xlink:to="lab_srt_MinimumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_ad254b92-db4b-4818-bc71-415cd06c8ae6_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property and equipment, net</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock_a97a5bde-8f63-4461-94ce-147a223ea208_terseLabel_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Business Combination</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock_label_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization Disclosure [Text Block]</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock_documentation_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:href="tlsi-20230930.xsd#tlsi_ReverseRecapitalizationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:to="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock_ac1a1a9b-eb6e-4198-8617-5cca877c7348_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Warrants Outstanding</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Stockholders' Equity Note, Warrants or Rights [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock" xlink:to="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsAbstract_166ffcdc-c93d-46c3-abbf-15db4b8c326d_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExercisePriceMember_5ae0077d-f545-4354-ac51-63ede3dbb2b4_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series&#160;B-3 Warrants exercise price per share</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExercisePriceMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Input, Exercise Price [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExercisePriceMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputExercisePriceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExercisePriceMember" xlink:to="lab_us-gaap_MeasurementInputExercisePriceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_87ca442f-2157-4826-8e8f-24297133365b_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">ROU assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (Decrease) in Operating Lease Liability</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAbstract"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss"/>
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    <link:label id="lab_tlsi_IncomeLossFromPreferredStockConvertibleDownRoundFeaturePerBasicShare_bc5805be-a755-4363-92e0-65c5404de9da_terseLabel_en-US" xlink:label="lab_tlsi_IncomeLossFromPreferredStockConvertibleDownRoundFeaturePerBasicShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase in net loss per common share, deemed dividend (in dollars per share)</link:label>
    <link:label id="lab_tlsi_IncomeLossFromPreferredStockConvertibleDownRoundFeaturePerBasicShare_label_en-US" xlink:label="lab_tlsi_IncomeLossFromPreferredStockConvertibleDownRoundFeaturePerBasicShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (Loss) from Preferred Stock, Convertible, Down Round Feature, Per Basic Share</link:label>
    <link:label id="lab_tlsi_IncomeLossFromPreferredStockConvertibleDownRoundFeaturePerBasicShare_documentation_en-US" xlink:label="lab_tlsi_IncomeLossFromPreferredStockConvertibleDownRoundFeaturePerBasicShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income (Loss) from Preferred Stock, Convertible, Down Round Feature, Per Basic Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_IncomeLossFromPreferredStockConvertibleDownRoundFeaturePerBasicShare" xlink:href="tlsi-20230930.xsd#tlsi_IncomeLossFromPreferredStockConvertibleDownRoundFeaturePerBasicShare"/>
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    <link:label id="lab_tlsi_ClassOfWarrantOrRightRepurchaseProgramAuthorizedAmount_5907fb34-e11d-47b7-9891-50fb422880e6_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRepurchaseProgramAuthorizedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrant repurchase program, authorized amount</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightRepurchaseProgramAuthorizedAmount_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRepurchaseProgramAuthorizedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class Of Warrant Or Right, Repurchase Program, Authorized Amount</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightRepurchaseProgramAuthorizedAmount_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRepurchaseProgramAuthorizedAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class Of Warrant Or Right, Repurchase Program, Authorized Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightRepurchaseProgramAuthorizedAmount" xlink:href="tlsi-20230930.xsd#tlsi_ClassOfWarrantOrRightRepurchaseProgramAuthorizedAmount"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_25fc6581-0594-4e6e-a2ee-32a400484e23_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net cash provided by financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Cash Provided by (Used in) Financing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases_a05253d8-cf78-4097-ba43-0907807e146f_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Final net exercise</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability, Purchases</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases"/>
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    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_156296ad-1c06-4dbf-a4a6-8e0a733dc234_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commitments and Contingencies</link:label>
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    <link:label id="lab_tlsi_SeriesB3ConvertiblePreferredStockMember_012ec408-e2d7-44cd-90a6-71edf71a942f_terseLabel_en-US" xlink:label="lab_tlsi_SeriesB3ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B-3</link:label>
    <link:label id="lab_tlsi_SeriesB3ConvertiblePreferredStockMember_label_en-US" xlink:label="lab_tlsi_SeriesB3ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B-3 Convertible Preferred Stock [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SeriesB3ConvertiblePreferredStockMember" xlink:href="tlsi-20230930.xsd#tlsi_SeriesB3ConvertiblePreferredStockMember"/>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_95eca61d-2add-4bcc-8a39-d21010008c42_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retained Earnings [Member]</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_255fdc2b-16c8-4b91-a6af-409588183b29_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total liabilities and stockholders&#8217; equity (deficit)</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
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    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_71c799cc-cd23-440a-aae6-b5a6b0725cf1_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssetsNoncurrent_label_en-US" xlink:label="lab_us-gaap_OtherAssetsNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Other Assets, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssetsNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherAssetsNoncurrent"/>
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    <link:label id="lab_tlsi_GainLossOnMilestonePaymentForAssetAcquistion_21608085-8b6c-4bc8-9d3e-091228e6d424_negatedTerseLabel_en-US" xlink:label="lab_tlsi_GainLossOnMilestonePaymentForAssetAcquistion" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Milestone payments to Dynavax</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_tlsi_GainLossOnMilestonePaymentForAssetAcquistion" xlink:href="tlsi-20230930.xsd#tlsi_GainLossOnMilestonePaymentForAssetAcquistion"/>
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    <link:label id="lab_us-gaap_EarningsPerShareBasic_b89669f8-d5eb-454e-9c2e-4a2cca490725_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net loss per share, basic (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnings Per Share, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EarningsPerShareBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareBasic" xlink:to="lab_us-gaap_EarningsPerShareBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_d32a31ff-a4dc-44f6-bcb1-234fbed7af22_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Right-of-use assets</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_a7ea4d86-469b-4560-b280-13022ff7245d_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Unrecognized compensation expense, options</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:to="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedStockOptions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate_ce2a24a0-723a-4dd1-b266-cf92d9dab4e1_terseLabel_en-US" xlink:label="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase agreement, sales price, percentage of market price</link:label>
    <link:label id="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate_label_en-US" xlink:label="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share Price As Percentage Of Market Price Commencing On Advance Notice Date</link:label>
    <link:label id="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate_documentation_en-US" xlink:label="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share Price As Percentage Of Market Price Commencing On Advance Notice Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:href="tlsi-20230930.xsd#tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:to="lab_tlsi_SharePriceAsPercentageOfMarketPriceCommencingOnAdvanceNoticeDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_627e82b0-d1a5-4f17-be47-5efe26e25484_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNameOfTransactionDomain_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of Stock [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SaleOfStockNameOfTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:to="lab_us-gaap_SaleOfStockNameOfTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstandingTerm_e7ec1a6a-8b20-4044-94ed-f59330e1c14c_verboseLabel_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Public warrants, term</link:label>
    <link:label id="lab_us-gaap_WarrantsAndRightsOutstandingTerm_label_en-US" xlink:label="lab_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrants and Rights Outstanding, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WarrantsAndRightsOutstandingTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:to="lab_us-gaap_WarrantsAndRightsOutstandingTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_22343971-4d40-407e-8ca5-f78fd066a906_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrants to purchase Series B-3 preferred stock (in shares)</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right, Number of Securities Called by Warrants or Rights</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:to="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByWarrantsOrRights" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockPercentageOfSharesCommitted_8cd6de2f-b0b6-4698-b7df-a78c10e10a90_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockPercentageOfSharesCommitted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Percentage of shares committed</link:label>
    <link:label id="lab_tlsi_PreferredStockPercentageOfSharesCommitted_label_en-US" xlink:label="lab_tlsi_PreferredStockPercentageOfSharesCommitted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Percentage of Shares Committed</link:label>
    <link:label id="lab_tlsi_PreferredStockPercentageOfSharesCommitted_documentation_en-US" xlink:label="lab_tlsi_PreferredStockPercentageOfSharesCommitted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Percentage of Shares Committed</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockPercentageOfSharesCommitted" xlink:href="tlsi-20230930.xsd#tlsi_PreferredStockPercentageOfSharesCommitted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockPercentageOfSharesCommitted" xlink:to="lab_tlsi_PreferredStockPercentageOfSharesCommitted" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_5615e3bf-a7d9-4184-865b-824c1fb37dda_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_69c3f2e6-f6a5-422b-a7f7-15e7524e1209_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Restricted Cash</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Restrictions on Cash and Cash Equivalents [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfRestrictedCashAndCashEquivalentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_bb7b1a14-a8c8-4ccd-88aa-8743c6910de0_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Net Cash Provided by (Used in) Investing Activities, Continuing Operations [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentTransitionReport_e5a4828d-440a-4445-a7d3-ccf0a3630b1e_terseLabel_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Transition Report</link:label>
    <link:label id="lab_dei_DocumentTransitionReport_label_en-US" xlink:label="lab_dei_DocumentTransitionReport" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Transition Report</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentTransitionReport" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentTransitionReport"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentTransitionReport" xlink:to="lab_dei_DocumentTransitionReport" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommercialMilestoneFirstCommercialSaleOfProductMember_d494f51b-3bba-46d3-90c0-d8cc3900252d_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestoneFirstCommercialSaleOfProductMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, First Commercial Sale of Product</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneFirstCommercialSaleOfProductMember_label_en-US" xlink:label="lab_tlsi_CommercialMilestoneFirstCommercialSaleOfProductMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, First Commercial Sale of Product [Member]</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneFirstCommercialSaleOfProductMember_documentation_en-US" xlink:label="lab_tlsi_CommercialMilestoneFirstCommercialSaleOfProductMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, First Commercial Sale of Product</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestoneFirstCommercialSaleOfProductMember" xlink:href="tlsi-20230930.xsd#tlsi_CommercialMilestoneFirstCommercialSaleOfProductMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommercialMilestoneFirstCommercialSaleOfProductMember" xlink:to="lab_tlsi_CommercialMilestoneFirstCommercialSaleOfProductMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_9aa1d6e0-2c1b-4f79-8bdf-12868dec0ec5_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_8fa72a3e-b1ff-4a11-8aff-36f2a3891a49_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative liability, measurement input</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Liability, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeLiabilityMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:to="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_TrancheAxis_9d538f5e-8bc0-4472-8552-962084d8d640_terseLabel_en-US" xlink:label="lab_tlsi_TrancheAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche [Axis]</link:label>
    <link:label id="lab_tlsi_TrancheAxis_label_en-US" xlink:label="lab_tlsi_TrancheAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche [Axis]</link:label>
    <link:label id="lab_tlsi_TrancheAxis_documentation_en-US" xlink:label="lab_tlsi_TrancheAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_TrancheAxis" xlink:href="tlsi-20230930.xsd#tlsi_TrancheAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_TrancheAxis" xlink:to="lab_tlsi_TrancheAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentInformationTable_709ea6a1-473e-4d15-9846-fbbd77d34406_terseLabel_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Information [Table]</link:label>
    <link:label id="lab_dei_DocumentInformationTable_label_en-US" xlink:label="lab_dei_DocumentInformationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Information [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentInformationTable" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentInformationTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentInformationTable" xlink:to="lab_dei_DocumentInformationTable" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ProceedsFromRefundablePrepaymentsForPreferredStock_1591b880-e912-4708-a12e-15d2e1c66564_terseLabel_en-US" xlink:label="lab_tlsi_ProceedsFromRefundablePrepaymentsForPreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Refundable prepayments for Series B-2 preferred stock</link:label>
    <link:label id="lab_tlsi_ProceedsFromRefundablePrepaymentsForPreferredStock_label_en-US" xlink:label="lab_tlsi_ProceedsFromRefundablePrepaymentsForPreferredStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds From Refundable Prepayments for Preferred Stock</link:label>
    <link:label id="lab_tlsi_ProceedsFromRefundablePrepaymentsForPreferredStock_documentation_en-US" xlink:label="lab_tlsi_ProceedsFromRefundablePrepaymentsForPreferredStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds From Refundable Prepayments for Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ProceedsFromRefundablePrepaymentsForPreferredStock" xlink:href="tlsi-20230930.xsd#tlsi_ProceedsFromRefundablePrepaymentsForPreferredStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ProceedsFromRefundablePrepaymentsForPreferredStock" xlink:to="lab_tlsi_ProceedsFromRefundablePrepaymentsForPreferredStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_0c5ae570-2fa9-466b-9474-8c496de98e80_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_TrancheAndWarrantLiabilityMember_a1cf8f89-589a-466c-b6c5-48724f2a9589_terseLabel_en-US" xlink:label="lab_tlsi_TrancheAndWarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche and warrant liability</link:label>
    <link:label id="lab_tlsi_TrancheAndWarrantLiabilityMember_label_en-US" xlink:label="lab_tlsi_TrancheAndWarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche and Warrant Liability [Member]</link:label>
    <link:label id="lab_tlsi_TrancheAndWarrantLiabilityMember_documentation_en-US" xlink:label="lab_tlsi_TrancheAndWarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche and Warrant Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_TrancheAndWarrantLiabilityMember" xlink:href="tlsi-20230930.xsd#tlsi_TrancheAndWarrantLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_TrancheAndWarrantLiabilityMember" xlink:to="lab_tlsi_TrancheAndWarrantLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_139d34cb-589d-46c9-8e33-080b035c13d9_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeInstrumentRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentRiskAxis" xlink:to="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ReverseRecapitalizationStockValueIfConvertedAmount_bdc746fc-cdaa-4da5-b51f-42c2235b6250_terseLabel_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationStockValueIfConvertedAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Enterprise value</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationStockValueIfConvertedAmount_label_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationStockValueIfConvertedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization, Stock Value, If-Converted Amount</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationStockValueIfConvertedAmount_documentation_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationStockValueIfConvertedAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Enterprise Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationStockValueIfConvertedAmount" xlink:href="tlsi-20230930.xsd#tlsi_ReverseRecapitalizationStockValueIfConvertedAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ReverseRecapitalizationStockValueIfConvertedAmount" xlink:to="lab_tlsi_ReverseRecapitalizationStockValueIfConvertedAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_1f9c5498-18f3-476b-a580-01d94331a3e6_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Adjustments to reconcile net loss to net cash used in operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_b2c06401-df1e-469d-969d-4eb2530b4dfc_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Liability Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueByLiabilityClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByLiabilityClassAxis" xlink:to="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_149c4300-1cd2-47b5-9575-91584a14d150_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_27fedd74-3be4-4a55-b981-d050542d1a03_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod_a185fb0f-bbc4-4742-b5f1-46170024cf27_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative instrument, contingent consideration, liability, earnout period</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:to="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StockIssuedDuringPeriodValueReverseRecapitalization_3e938296-b3c9-41b6-8a09-f58b2ea7c0c7_terseLabel_en-US" xlink:label="lab_tlsi_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Issuance of common stock upon closing the Business Combination, net of expenses</link:label>
    <link:label id="lab_tlsi_StockIssuedDuringPeriodValueReverseRecapitalization_label_en-US" xlink:label="lab_tlsi_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock Issued During Period, Value, Reverse Recapitalization</link:label>
    <link:label id="lab_tlsi_StockIssuedDuringPeriodValueReverseRecapitalization_documentation_en-US" xlink:label="lab_tlsi_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock Issued During Period, Value, Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:href="tlsi-20230930.xsd#tlsi_StockIssuedDuringPeriodValueReverseRecapitalization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:to="lab_tlsi_StockIssuedDuringPeriodValueReverseRecapitalization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_54a89b3e-cf76-4f56-a386-b04b20194d4e_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsequentEventTypeAxis_label_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Subsequent Event Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SubsequentEventTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SubsequentEventTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SubsequentEventTypeAxis" xlink:to="lab_us-gaap_SubsequentEventTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromStockOptionsExercised_0a21672e-abef-4207-beaa-bfa08918db46_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash proceeds from the exercise of stock options</link:label>
    <link:label id="lab_us-gaap_ProceedsFromStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_ProceedsFromStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Stock Options Exercised</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromStockOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromStockOptionsExercised" xlink:to="lab_us-gaap_ProceedsFromStockOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold_56c843b6-010d-408c-82db-1959e920867c_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrant redemption condition, share price (in dollars per share)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class Of Warrant Or Right, Conversion Stock Price Threshold</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class Of Warrant Or Right, Conversion Stock Price Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:href="tlsi-20230930.xsd#tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:to="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember_980d52c3-9b87-44d5-8f79-fb9b71284984_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series&#160;B-3 Warrant liabilities</link:label>
    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember_26eeb013-3be2-4708-9524-fa3adf646c4a_verboseLabel_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B-3 Warrants</link:label>
    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember_label_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Financial Instruments, Series B-3 Warrant Liability [Member]</link:label>
    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember_documentation_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Financial Instruments, Series B-3 Warrant Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember" xlink:to="lab_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SeriesA1ConvertiblePreferredStockMember_8c06681a-fb13-4972-a320-f1d1663e2fb2_terseLabel_en-US" xlink:label="lab_tlsi_SeriesA1ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-1</link:label>
    <link:label id="lab_tlsi_SeriesA1ConvertiblePreferredStockMember_label_en-US" xlink:label="lab_tlsi_SeriesA1ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-1 Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_tlsi_SeriesA1ConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_tlsi_SeriesA1ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-1 Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SeriesA1ConvertiblePreferredStockMember" xlink:href="tlsi-20230930.xsd#tlsi_SeriesA1ConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SeriesA1ConvertiblePreferredStockMember" xlink:to="lab_tlsi_SeriesA1ConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ConvertibleNotesAndWarrantsMember_451f0a16-e8a4-444e-9b56-188557af7054_terseLabel_en-US" xlink:label="lab_tlsi_ConvertibleNotesAndWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Convertible notes and warrants</link:label>
    <link:label id="lab_tlsi_ConvertibleNotesAndWarrantsMember_label_en-US" xlink:label="lab_tlsi_ConvertibleNotesAndWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Convertible Notes and Warrants [Member]</link:label>
    <link:label id="lab_tlsi_ConvertibleNotesAndWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_ConvertibleNotesAndWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Convertible Notes and Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ConvertibleNotesAndWarrantsMember" xlink:href="tlsi-20230930.xsd#tlsi_ConvertibleNotesAndWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ConvertibleNotesAndWarrantsMember" xlink:to="lab_tlsi_ConvertibleNotesAndWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharePrice_96b57997-4d13-4013-866c-ca9390cc59cb_terseLabel_en-US" xlink:label="lab_us-gaap_SharePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Closing price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_SharePrice_label_en-US" xlink:label="lab_us-gaap_SharePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Share Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SharePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharePrice" xlink:to="lab_us-gaap_SharePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_A2009PlanMember_959445f6-dd20-4cec-b5cf-f28c1d1c819b_terseLabel_en-US" xlink:label="lab_tlsi_A2009PlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2009 Plan</link:label>
    <link:label id="lab_tlsi_A2009PlanMember_label_en-US" xlink:label="lab_tlsi_A2009PlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2009 Plan [Member]</link:label>
    <link:label id="lab_tlsi_A2009PlanMember_documentation_en-US" xlink:label="lab_tlsi_A2009PlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2009 Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_A2009PlanMember" xlink:href="tlsi-20230930.xsd#tlsi_A2009PlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_A2009PlanMember" xlink:to="lab_tlsi_A2009PlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodAxis_a8e59bb2-0b81-4502-9700-0b839c9fac4c_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period [Axis]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodAxis_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period [Axis]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodAxis_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodAxis" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeInstrumentPeriodAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentPeriodAxis" xlink:to="lab_tlsi_DerivativeInstrumentPeriodAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityTableTextBlock_d5d0f47e-dbf1-4924-8ce5-394e9f28d0f8_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Schedule of Convertible Preferred Stock</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Temporary Equity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityTableTextBlock" xlink:to="lab_us-gaap_TemporaryEquityTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionOfConvertibleSecurities_634fc3ed-7cc5-4a06-9be7-3fb5c7155839_negatedTerseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Retirements/Conversion (in shares)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant Or Right, Conversion Of Convertible Securities</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionOfConvertibleSecurities_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant Or Right, Conversion Of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightConversionOfConvertibleSecurities" xlink:href="tlsi-20230930.xsd#tlsi_ClassOfWarrantOrRightConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightConversionOfConvertibleSecurities" xlink:to="lab_tlsi_ClassOfWarrantOrRightConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_dba39b7c-0f46-4f39-aaaa-0c65e28d7e1e_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightOutstandingWarrantsIssuedDuringPeriodNewIssues_b079b3fc-c234-4d6b-9bd9-3631aef607b5_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightOutstandingWarrantsIssuedDuringPeriodNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Issuances (in shares)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightOutstandingWarrantsIssuedDuringPeriodNewIssues_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightOutstandingWarrantsIssuedDuringPeriodNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class Of Warrant Or Right Outstanding, Warrants Issued During Period, New Issues</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightOutstandingWarrantsIssuedDuringPeriodNewIssues_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightOutstandingWarrantsIssuedDuringPeriodNewIssues" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class Of Warrant Or Right Outstanding, Warrants Issued During Period, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightOutstandingWarrantsIssuedDuringPeriodNewIssues" xlink:href="tlsi-20230930.xsd#tlsi_ClassOfWarrantOrRightOutstandingWarrantsIssuedDuringPeriodNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightOutstandingWarrantsIssuedDuringPeriodNewIssues" xlink:to="lab_tlsi_ClassOfWarrantOrRightOutstandingWarrantsIssuedDuringPeriodNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SeriesA2ConvertiblePreferredStockMember_b8743189-fb3d-4276-9ccc-f97a3e17c6fb_terseLabel_en-US" xlink:label="lab_tlsi_SeriesA2ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-2</link:label>
    <link:label id="lab_tlsi_SeriesA2ConvertiblePreferredStockMember_label_en-US" xlink:label="lab_tlsi_SeriesA2ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-2 Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_tlsi_SeriesA2ConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_tlsi_SeriesA2ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-2 Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SeriesA2ConvertiblePreferredStockMember" xlink:href="tlsi-20230930.xsd#tlsi_SeriesA2ConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SeriesA2ConvertiblePreferredStockMember" xlink:to="lab_tlsi_SeriesA2ConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_GainLossOnEquityIssuance_61dbbe83-f510-452e-be73-bb1403cac235_terseLabel_en-US" xlink:label="lab_tlsi_GainLossOnEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Loss on equity issuance</link:label>
    <link:label id="lab_tlsi_GainLossOnEquityIssuance_1648baec-a589-421b-afe9-5bb384345a66_negatedTerseLabel_en-US" xlink:label="lab_tlsi_GainLossOnEquityIssuance" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Loss on equity issuance</link:label>
    <link:label id="lab_tlsi_GainLossOnEquityIssuance_label_en-US" xlink:label="lab_tlsi_GainLossOnEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gain (Loss) on Equity Issuance</link:label>
    <link:label id="lab_tlsi_GainLossOnEquityIssuance_documentation_en-US" xlink:label="lab_tlsi_GainLossOnEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gain (Loss) on Equity Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_GainLossOnEquityIssuance" xlink:href="tlsi-20230930.xsd#tlsi_GainLossOnEquityIssuance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_GainLossOnEquityIssuance" xlink:to="lab_tlsi_GainLossOnEquityIssuance" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PublicWarrantsMember_1ffc0ba5-5d1e-4de5-a53c-977ebdab20da_terseLabel_en-US" xlink:label="lab_tlsi_PublicWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Public Warrants</link:label>
    <link:label id="lab_tlsi_PublicWarrantsMember_label_en-US" xlink:label="lab_tlsi_PublicWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Public Warrants [Member]</link:label>
    <link:label id="lab_tlsi_PublicWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_PublicWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Public Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PublicWarrantsMember" xlink:href="tlsi-20230930.xsd#tlsi_PublicWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PublicWarrantsMember" xlink:to="lab_tlsi_PublicWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentPeriodEndDate_9454f277-8b14-42fc-b8fe-68a85f889890_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Period End Date</link:label>
    <link:label id="lab_dei_DocumentPeriodEndDate_label_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Document Period End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentPeriodEndDate" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentPeriodEndDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentPeriodEndDate" xlink:to="lab_dei_DocumentPeriodEndDate" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SaleOfStockAuthorizedAmountValue_239ee900-6076-4b4d-9ae3-1c94688e910e_terseLabel_en-US" xlink:label="lab_tlsi_SaleOfStockAuthorizedAmountValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale of stock, authorized amount</link:label>
    <link:label id="lab_tlsi_SaleOfStockAuthorizedAmountValue_label_en-US" xlink:label="lab_tlsi_SaleOfStockAuthorizedAmountValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale Of Stock, Authorized Amount, Value</link:label>
    <link:label id="lab_tlsi_SaleOfStockAuthorizedAmountValue_documentation_en-US" xlink:label="lab_tlsi_SaleOfStockAuthorizedAmountValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sale Of Stock, Authorized Amount, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SaleOfStockAuthorizedAmountValue" xlink:href="tlsi-20230930.xsd#tlsi_SaleOfStockAuthorizedAmountValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SaleOfStockAuthorizedAmountValue" xlink:to="lab_tlsi_SaleOfStockAuthorizedAmountValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_e3f296de-b43c-4419-86cc-a34ee5455551_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock, dividend rate, percentage</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendRatePercentage_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Dividend Rate, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockDividendRatePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendRatePercentage" xlink:to="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockTextBlock_42f277fe-cf72-48e4-9437-7d3463c1e271_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockTextBlock_label_en-US" xlink:label="lab_us-gaap_PreferredStockTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockTextBlock" xlink:to="lab_us-gaap_PreferredStockTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ValuationReverseRecapitalizationApproachEnterpriseValueMember_00c4cc63-107f-4d39-a6d1-22972fae3c91_terseLabel_en-US" xlink:label="lab_tlsi_ValuationReverseRecapitalizationApproachEnterpriseValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Valuation, Reverse Recapitalization Approach, Enterprise Value</link:label>
    <link:label id="lab_tlsi_ValuationReverseRecapitalizationApproachEnterpriseValueMember_label_en-US" xlink:label="lab_tlsi_ValuationReverseRecapitalizationApproachEnterpriseValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Valuation, Reverse Recapitalization Approach, Enterprise Value [Member]</link:label>
    <link:label id="lab_tlsi_ValuationReverseRecapitalizationApproachEnterpriseValueMember_documentation_en-US" xlink:label="lab_tlsi_ValuationReverseRecapitalizationApproachEnterpriseValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Valuation, Reverse Recapitalization Approach, Enterprise Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ValuationReverseRecapitalizationApproachEnterpriseValueMember" xlink:href="tlsi-20230930.xsd#tlsi_ValuationReverseRecapitalizationApproachEnterpriseValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ValuationReverseRecapitalizationApproachEnterpriseValueMember" xlink:to="lab_tlsi_ValuationReverseRecapitalizationApproachEnterpriseValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AssetAcquisitionSalesMilestone_8d662fc3-e689-4e04-accd-2f7e74d0849f_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionSalesMilestone" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Sales milestone</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionSalesMilestone_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionSalesMilestone" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Sales Milestone</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionSalesMilestone_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionSalesMilestone" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Sales Milestone</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionSalesMilestone" xlink:href="tlsi-20230930.xsd#tlsi_AssetAcquisitionSalesMilestone"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionSalesMilestone" xlink:to="lab_tlsi_AssetAcquisitionSalesMilestone" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AssetAcquisitionMilestoneAmount_e5b226ef-bf42-4fb3-9110-009a95ae8703_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Milestone amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionMilestoneAmount_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Milestone, Amount</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionMilestoneAmount_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Milestone, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionMilestoneAmount" xlink:href="tlsi-20230930.xsd#tlsi_AssetAcquisitionMilestoneAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionMilestoneAmount" xlink:to="lab_tlsi_AssetAcquisitionMilestoneAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_e13690ed-68b7-4e25-8f63-bd78eae4bf69_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_e98780df-1929-4e80-a9a2-67706a4b124e_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightAxis_label_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Class of Warrant or Right [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfWarrantOrRightAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ClassOfWarrantOrRightAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfWarrantOrRightAxis" xlink:to="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_ecc3da84-f108-4ab5-b229-f52a1166606e_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gain (loss) on derivatives</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_5c806dca-731d-49f1-b3e8-e97749f239f4_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Change in fair value of derivative liability</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_eeb36ea2-1228-41e6-8d79-e796249b08bc_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Loss on equity issuance</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_label_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative, Gain (Loss) on Derivative, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeGainLossOnDerivativeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:to="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_59bc71d9-e468-469c-aebd-12855b0ddecd_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Loss on disposal of fixed assets</link:label>
    <link:label id="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment_label_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gain (Loss) on Disposition of Property Plant Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GainLossOnSaleOfPropertyPlantEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:to="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesAuthorized_f1f69905-dab7-4aea-b852-0cc5a48ecc65_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Convertible preferred stock, shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesAuthorized_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Temporary Equity, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquitySharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesAuthorized" xlink:to="lab_us-gaap_TemporaryEquitySharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_97500c78-6a43-41fc-9154-2073bc912476_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryFinishedGoodsNetOfReserves_2cb593a5-fd15-4ebc-a2dd-23c89a55d7da_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Finished goods</link:label>
    <link:label id="lab_us-gaap_InventoryFinishedGoodsNetOfReserves_label_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory, Finished Goods, Net of Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryFinishedGoodsNetOfReserves"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:to="lab_us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_27f5f380-b55f-45ff-88b9-cfd51f860c4d_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ReverseRecapitalizationTransactionCostsPaid_e1abbfbf-3fa6-4a7c-961d-d1874ab4dff5_terseLabel_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationTransactionCostsPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Transaction costs paid from proceeds</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationTransactionCostsPaid_label_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationTransactionCostsPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization, Transaction Costs Paid</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationTransactionCostsPaid_documentation_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationTransactionCostsPaid" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization, Transaction Costs Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationTransactionCostsPaid" xlink:href="tlsi-20230930.xsd#tlsi_ReverseRecapitalizationTransactionCostsPaid"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ReverseRecapitalizationTransactionCostsPaid" xlink:to="lab_tlsi_ReverseRecapitalizationTransactionCostsPaid" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_7ca589c7-b812-4b39-b4d0-8346da6c2e71_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockWarrantMember_b03972f7-9ea6-4ad3-b35c-0d7b057d5c20_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred stock warrants</link:label>
    <link:label id="lab_tlsi_PreferredStockWarrantMember_label_en-US" xlink:label="lab_tlsi_PreferredStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock Warrant [Member]</link:label>
    <link:label id="lab_tlsi_PreferredStockWarrantMember_documentation_en-US" xlink:label="lab_tlsi_PreferredStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock Warrant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockWarrantMember" xlink:href="tlsi-20230930.xsd#tlsi_PreferredStockWarrantMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockWarrantMember" xlink:to="lab_tlsi_PreferredStockWarrantMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentEarnoutLiabilityMember_75eb0923-d251-4d30-b293-e726ac616a9c_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentEarnoutLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Contingent earnout liability</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentEarnoutLiabilityMember_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentEarnoutLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Earnout Liability [Member]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentEarnoutLiabilityMember_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentEarnoutLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Earnout Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentContingentEarnoutLiabilityMember" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeInstrumentContingentEarnoutLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentContingentEarnoutLiabilityMember" xlink:to="lab_tlsi_DerivativeInstrumentContingentEarnoutLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_92251f3d-657b-4eea-9441-642b53db526b_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of operating segments</link:label>
    <link:label id="lab_us-gaap_NumberOfOperatingSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfOperatingSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of Operating Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfOperatingSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NumberOfOperatingSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfOperatingSegments" xlink:to="lab_us-gaap_NumberOfOperatingSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAbstract_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash and Cash Equivalents [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashAndCashEquivalentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAbstract" xlink:to="lab_us-gaap_CashAndCashEquivalentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodOneMember_f5ee7c06-35f0-4542-af8c-5da70c0c7a12_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche One</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodOneMember_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period One [Member]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodOneMember_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodOneMember" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeInstrumentPeriodOneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentPeriodOneMember" xlink:to="lab_tlsi_DerivativeInstrumentPeriodOneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_985ef054-938f-4468-a167-6ba600c24ff6_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assumption of preferred stock in connection with the Business Combination</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_dffa343c-daa9-437f-9999-cecab437a003_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Issuance of stock</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock Issued During Period, Value, New Issues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodValueNewIssues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityAbstract_272a4881-33e1-4f0e-bba1-c29f4bbf1033_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stockholders&#8217; equity (deficit):</link:label>
    <link:label id="lab_us-gaap_EquityAbstract_label_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityAbstract" xlink:to="lab_us-gaap_EquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InventoryDisclosureTextBlock_9446f505-14a0-4698-9c05-ae98ebedf855_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory</link:label>
    <link:label id="lab_us-gaap_InventoryDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_InventoryDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Inventory Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InventoryDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_InventoryDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InventoryDisclosureTextBlock" xlink:to="lab_us-gaap_InventoryDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_9df76131-8546-43c9-8125-b45a0cefcc4c_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue</link:label>
    <link:label id="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax_label_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Revenue from Contract with Customer, Excluding Assessed Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:to="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_c83aded2-2151-4fa0-bdd8-572bea01ad2f_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_2c0fc07a-04c6-4755-bf55-e1ebe83ace44_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Undeclared dividends on Series A preferred stock</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_8bfcb00b-0ea2-43b8-8ba2-de86f17cd494_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Undeclared dividends</link:label>
    <link:label id="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact_label_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock Dividends, Income Statement Impact</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockDividendsIncomeStatementImpact"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:to="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockRedemptionPricePerShare_4c3aa2f1-680a-4598-b9b8-ee09e3682609_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Conversion price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_PreferredStockRedemptionPricePerShare_label_en-US" xlink:label="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Redemption Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockRedemptionPricePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockRedemptionPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockRedemptionPricePerShare" xlink:to="lab_us-gaap_PreferredStockRedemptionPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_33c40f5a-ee6a-40a3-a39f-4978b4c0eb21_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Amendment Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AmendmentFlag" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_AmendmentFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_AmendmentFlag" xlink:to="lab_dei_AmendmentFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger_64161e66-2fa5-4ce8-bd3a-9883f1662e50_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnout shares vesting requirement, weighted average price per share (in dollars per share)</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Stock Price Trigger</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Stock Price Trigger</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:to="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_73ace2da-8233-4303-a4f1-e19f56819d8e_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Convertible preferred stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesOutstanding_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Temporary Equity, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquitySharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesOutstanding" xlink:to="lab_us-gaap_TemporaryEquitySharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_6e38098e-a4fa-4605-b97b-b6689f3aab5e_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_LegalEntityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice_8bc7cfb7-0208-4e96-af7a-f7f71243ecd0_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of trading days, VWAP</link:label>
    <link:label id="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice_label_en-US" xlink:label="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Number of Trading Days, Volume Weighted Average Price</link:label>
    <link:label id="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice_documentation_en-US" xlink:label="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Number of Trading Days, Volume Weighted Average Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:href="tlsi-20230930.xsd#tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:to="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_MeasurementInputFairValueSharePriceMember_43645711-59c4-4cb0-abfa-8da0fce7ffe0_terseLabel_en-US" xlink:label="lab_tlsi_MeasurementInputFairValueSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B-2, B-3 preferred stock fair value per share</link:label>
    <link:label id="lab_tlsi_MeasurementInputFairValueSharePriceMember_2e0afe44-c48a-4284-9446-81a37560d4fe_verboseLabel_en-US" xlink:label="lab_tlsi_MeasurementInputFairValueSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series B-3 preferred stock fair value per share</link:label>
    <link:label id="lab_tlsi_MeasurementInputFairValueSharePriceMember_label_en-US" xlink:label="lab_tlsi_MeasurementInputFairValueSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Input, Fair Value Share Price [Member]</link:label>
    <link:label id="lab_tlsi_MeasurementInputFairValueSharePriceMember_documentation_en-US" xlink:label="lab_tlsi_MeasurementInputFairValueSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Measurement Input, Fair Value Share Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_MeasurementInputFairValueSharePriceMember" xlink:href="tlsi-20230930.xsd#tlsi_MeasurementInputFairValueSharePriceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_MeasurementInputFairValueSharePriceMember" xlink:to="lab_tlsi_MeasurementInputFairValueSharePriceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_A2023PlanMember_134106c4-e899-4ba6-b689-aef5a4df5d08_terseLabel_en-US" xlink:label="lab_tlsi_A2023PlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2023 Plan</link:label>
    <link:label id="lab_tlsi_A2023PlanMember_label_en-US" xlink:label="lab_tlsi_A2023PlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2023 Plan [Member]</link:label>
    <link:label id="lab_tlsi_A2023PlanMember_documentation_en-US" xlink:label="lab_tlsi_A2023PlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">2023 Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_A2023PlanMember" xlink:href="tlsi-20230930.xsd#tlsi_A2023PlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_A2023PlanMember" xlink:to="lab_tlsi_A2023PlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommercialMilestone250000AnnualSalesMember_d50dbb7d-5149-4b4a-928c-0e5f5fe613d9_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestone250000AnnualSalesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, $250,000 Annual Sales</link:label>
    <link:label id="lab_tlsi_CommercialMilestone250000AnnualSalesMember_label_en-US" xlink:label="lab_tlsi_CommercialMilestone250000AnnualSalesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, $250,000 Annual Sales [Member]</link:label>
    <link:label id="lab_tlsi_CommercialMilestone250000AnnualSalesMember_documentation_en-US" xlink:label="lab_tlsi_CommercialMilestone250000AnnualSalesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, $250,000 Annual Sales</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestone250000AnnualSalesMember" xlink:href="tlsi-20230930.xsd#tlsi_CommercialMilestone250000AnnualSalesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommercialMilestone250000AnnualSalesMember" xlink:to="lab_tlsi_CommercialMilestone250000AnnualSalesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommercialMilestoneMember_2119a09b-1cad-41de-ba08-670d55a86c57_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestoneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneMember_label_en-US" xlink:label="lab_tlsi_CommercialMilestoneMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone [Member]</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneMember_documentation_en-US" xlink:label="lab_tlsi_CommercialMilestoneMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestoneMember" xlink:href="tlsi-20230930.xsd#tlsi_CommercialMilestoneMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommercialMilestoneMember" xlink:to="lab_tlsi_CommercialMilestoneMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_f442a356-fbee-472d-8c4d-bf09cf883924_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash and Cash Equivalents, at Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset_1f2014ff-4674-4d3b-815e-f07118586c40_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Conversion price, first automatic reset</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset_label_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Conversion Price, Automatic Reset Duration, First Reset</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset_documentation_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Preferred Stock, Conversion Price, Automatic Reset Duration, First Reset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:href="tlsi-20230930.xsd#tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:to="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SeriesA6ConvertiblePreferredStockMember_ba5caf1e-5f03-4f6c-a1b8-5121a0fe3938_terseLabel_en-US" xlink:label="lab_tlsi_SeriesA6ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-6</link:label>
    <link:label id="lab_tlsi_SeriesA6ConvertiblePreferredStockMember_label_en-US" xlink:label="lab_tlsi_SeriesA6ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-6 Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_tlsi_SeriesA6ConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_tlsi_SeriesA6ConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A-6 Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SeriesA6ConvertiblePreferredStockMember" xlink:href="tlsi-20230930.xsd#tlsi_SeriesA6ConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SeriesA6ConvertiblePreferredStockMember" xlink:to="lab_tlsi_SeriesA6ConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_d846e249-13d0-4763-8d3d-bda4cdfb8bdf_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Convertible preferred stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_TemporaryEquitySharesIssued_label_en-US" xlink:label="lab_us-gaap_TemporaryEquitySharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Temporary Equity, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquitySharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquitySharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquitySharesIssued" xlink:to="lab_us-gaap_TemporaryEquitySharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PurchaseAgreementOwnershipLimitation_b7931802-d165-440b-b790-412a0f33b3e2_terseLabel_en-US" xlink:label="lab_tlsi_PurchaseAgreementOwnershipLimitation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase agreement, ownership limitation</link:label>
    <link:label id="lab_tlsi_PurchaseAgreementOwnershipLimitation_label_en-US" xlink:label="lab_tlsi_PurchaseAgreementOwnershipLimitation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase Agreement, Ownership Limitation</link:label>
    <link:label id="lab_tlsi_PurchaseAgreementOwnershipLimitation_documentation_en-US" xlink:label="lab_tlsi_PurchaseAgreementOwnershipLimitation" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase Agreement, Ownership Limitation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PurchaseAgreementOwnershipLimitation" xlink:href="tlsi-20230930.xsd#tlsi_PurchaseAgreementOwnershipLimitation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PurchaseAgreementOwnershipLimitation" xlink:to="lab_tlsi_PurchaseAgreementOwnershipLimitation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_8868e425-9ae0-4399-9679-19c6eb9620de_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, plant and equipment, useful life</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment, Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PropertyPlantAndEquipmentUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays_4aebd95f-7c8a-4f7d-a152-4793547ef5f9_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchase agreement, number of days used for measurement of average daily trading volume</link:label>
    <link:label id="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays_label_en-US" xlink:label="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock, Share Price, Average Daily Volume, Number Of Trading Days</link:label>
    <link:label id="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays_documentation_en-US" xlink:label="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Common Stock, Share Price, Average Daily Volume, Number Of Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:href="tlsi-20230930.xsd#tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:to="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_ec67e816-bac7-40bf-9878-e3f670dceb53_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted average common shares outstanding, diluted (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:to="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MoneyMarketFundsAtCarryingValue_9c13d621-f8fe-4620-b604-3057ae6f46f9_terseLabel_en-US" xlink:label="lab_us-gaap_MoneyMarketFundsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Investments in money market funds</link:label>
    <link:label id="lab_us-gaap_MoneyMarketFundsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_MoneyMarketFundsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Money Market Funds, at Carrying Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MoneyMarketFundsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_MoneyMarketFundsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MoneyMarketFundsAtCarryingValue" xlink:to="lab_us-gaap_MoneyMarketFundsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ReverseRecapitalizationAbstract_label_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization [Abstract]</link:label>
    <link:label id="lab_tlsi_ReverseRecapitalizationAbstract_documentation_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationAbstract" xlink:href="tlsi-20230930.xsd#tlsi_ReverseRecapitalizationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ReverseRecapitalizationAbstract" xlink:to="lab_tlsi_ReverseRecapitalizationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommercialMilestone500000AnnualSalesMember_7511d96b-f53f-4575-babd-70f12eaf4871_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestone500000AnnualSalesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, $500,000 Annual Sales</link:label>
    <link:label id="lab_tlsi_CommercialMilestone500000AnnualSalesMember_label_en-US" xlink:label="lab_tlsi_CommercialMilestone500000AnnualSalesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, $500,000 Annual Sales [Member]</link:label>
    <link:label id="lab_tlsi_CommercialMilestone500000AnnualSalesMember_documentation_en-US" xlink:label="lab_tlsi_CommercialMilestone500000AnnualSalesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone, $500,000 Annual Sales</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestone500000AnnualSalesMember" xlink:href="tlsi-20230930.xsd#tlsi_CommercialMilestone500000AnnualSalesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommercialMilestone500000AnnualSalesMember" xlink:to="lab_tlsi_CommercialMilestone500000AnnualSalesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_828d7a01-7a37-47a6-b54e-458c4b90cfa9_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating expenses:</link:label>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Operating Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpensesAbstract" xlink:to="lab_us-gaap_OperatingExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_13c73bb6-8a37-4798-bfa4-074b41863e2c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Purchases of property and equipment</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments to Acquire Property, Plant, and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PaymentsToAcquirePropertyPlantAndEquipment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:to="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_95b80b5a-07a1-48fd-80ab-0dfffe8f233b_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount_98dfff30-a23b-43e0-8218-0dccaee50e5c_terseLabel_en-US" xlink:label="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for milestone</link:label>
    <link:label id="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount_label_en-US" xlink:label="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for Asset Acquisition, Milestone Amount</link:label>
    <link:label id="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount_documentation_en-US" xlink:label="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Payments for Asset Acquisition, Milestone Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:href="tlsi-20230930.xsd#tlsi_PaymentsForAssetAcquisitionMilestoneAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:to="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_93e5969c-aec6-4092-b49d-90c30015c059_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfWarrants_4e1e11f4-601b-4e13-92e1-d3be15c695ee_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfWarrants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair value of warrant liability</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfWarrants_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfWarrants" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Issuance of Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfWarrants" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfWarrants"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfWarrants" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfWarrants" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_55e1ee1f-284a-420d-b1a0-17368cc38f8a_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Stock-based compensation</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:to="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommercialMilestoneTypeDomain_d9e9fcbf-399b-45a3-89d7-7713100fc7bb_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone Type [Domain]</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneTypeDomain_label_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone Type [Domain]</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneTypeDomain_documentation_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestoneTypeDomain" xlink:href="tlsi-20230930.xsd#tlsi_CommercialMilestoneTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommercialMilestoneTypeDomain" xlink:to="lab_tlsi_CommercialMilestoneTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodDomain_b09aaccd-2127-4b7e-826c-fbac79845a3c_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period [Domain]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodDomain_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period [Domain]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodDomain_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodDomain" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeInstrumentPeriodDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentPeriodDomain" xlink:to="lab_tlsi_DerivativeInstrumentPeriodDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_SeriesAConvertiblePreferredStockMember_0fa441be-1e9d-4e91-b6a2-be5314af4391_terseLabel_en-US" xlink:label="lab_tlsi_SeriesAConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A Convertible Preferred Stock</link:label>
    <link:label id="lab_tlsi_SeriesAConvertiblePreferredStockMember_label_en-US" xlink:label="lab_tlsi_SeriesAConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A Convertible Preferred Stock [Member]</link:label>
    <link:label id="lab_tlsi_SeriesAConvertiblePreferredStockMember_documentation_en-US" xlink:label="lab_tlsi_SeriesAConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series A Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SeriesAConvertiblePreferredStockMember" xlink:href="tlsi-20230930.xsd#tlsi_SeriesAConvertiblePreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SeriesAConvertiblePreferredStockMember" xlink:to="lab_tlsi_SeriesAConvertiblePreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LeaseLiabilityCurrent_8e679d45-61eb-4a2e-a768-6c40dc2880f3_terseLabel_en-US" xlink:label="lab_tlsi_LeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Short-term lease liabilities</link:label>
    <link:label id="lab_tlsi_LeaseLiabilityCurrent_label_en-US" xlink:label="lab_tlsi_LeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lease Liability, Current</link:label>
    <link:label id="lab_tlsi_LeaseLiabilityCurrent_documentation_en-US" xlink:label="lab_tlsi_LeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Lease Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LeaseLiabilityCurrent" xlink:href="tlsi-20230930.xsd#tlsi_LeaseLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LeaseLiabilityCurrent" xlink:to="lab_tlsi_LeaseLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommercialMilestoneTypeAxis_7f062e94-4877-49dc-b56c-3ba2893a14d3_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone Type [Axis]</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneTypeAxis_label_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone Type [Axis]</link:label>
    <link:label id="lab_tlsi_CommercialMilestoneTypeAxis_documentation_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Commercial Milestone Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestoneTypeAxis" xlink:href="tlsi-20230930.xsd#tlsi_CommercialMilestoneTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommercialMilestoneTypeAxis" xlink:to="lab_tlsi_CommercialMilestoneTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_82ee8681-c40f-4a4e-9ea6-83406b6abea3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Fair Value Measurement Inputs and Valuation Techniques [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_TrancheThreeMember_bf035381-fb09-49dd-b4fc-0601ae4607c7_terseLabel_en-US" xlink:label="lab_tlsi_TrancheThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche Three</link:label>
    <link:label id="lab_tlsi_TrancheThreeMember_label_en-US" xlink:label="lab_tlsi_TrancheThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche Three [Member]</link:label>
    <link:label id="lab_tlsi_TrancheThreeMember_documentation_en-US" xlink:label="lab_tlsi_TrancheThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_TrancheThreeMember" xlink:href="tlsi-20230930.xsd#tlsi_TrancheThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_TrancheThreeMember" xlink:to="lab_tlsi_TrancheThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferred_e1a2ecce-bd5c-4cb8-820d-fac046ab7c39_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Upfront payment</link:label>
    <link:label id="lab_us-gaap_AssetAcquisitionConsiderationTransferred_label_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Asset Acquisition, Consideration Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetAcquisitionConsiderationTransferred"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:to="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock_38a9324e-502e-41ef-a304-0ae4013935b3_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Cash and Cash Equivalents Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashAndCashEquivalentsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays_2dbb4b3d-a796-44f3-ae97-d7afcd4c0178_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Earnout period, threshold consecutive trading days</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Threshold Consecutive Trading Days</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Contingent Consideration, Liability, Earnout Period, Threshold Consecutive Trading Days</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:to="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_687dc8a1-5f4b-4c67-b076-56d70be51d08_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Increase (decrease) in cash, cash equivalents and restricted cash</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodThreeMember_4e54c650-47df-4745-8e6b-a9587f7c067c_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Tranche Three</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodThreeMember_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period Three [Member]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodThreeMember_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Instrument, Period Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeInstrumentPeriodThreeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:to="lab_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_b37d4af8-dcf5-49a6-b760-144d9566ba18_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Equity Component [Domain]</link:label>
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    <link:label id="lab_us-gaap_OperatingIncomeLoss_0ab6e29f-f68c-4727-941f-c664b0d82c70_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Loss from operations</link:label>
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    <link:label id="lab_tlsi_ProceedsFromReverseRecapitalization_d55543d5-7576-4998-a4b0-c9f496640689_terseLabel_en-US" xlink:label="lab_tlsi_ProceedsFromReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Proceeds from Business Combination</link:label>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities_c28ea0ce-7f81-40f1-8557-ad24464861fb_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Conversion of redeemable convertible preferred stock into common stock in connection with the Business Combination</link:label>
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    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMember_91f5cc56-5f57-4904-83b5-2000e1105b52_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Standby Equity Purchase Agreement</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMember_label_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Standby Equity Purchase Agreement [Member]</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMember_documentation_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Standby Equity Purchase Agreement</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_7ba7ffe2-325f-4164-a145-56060560da4a_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property and Equipment</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
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    <link:label id="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones_a05200fc-c040-4166-b748-2fd45631dca4_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Number of commercial milestones</link:label>
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    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsTrancheLiabilityMember_a7297025-6aeb-4226-9bd1-f45b346c196a_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsTrancheLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Series&#160;B-2 tranche liabilities</link:label>
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    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsTrancheLiabilityMember_documentation_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsTrancheLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Derivative Financial Instruments, Tranche Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeFinancialInstrumentsTrancheLiabilityMember" xlink:href="tlsi-20230930.xsd#tlsi_DerivativeFinancialInstrumentsTrancheLiabilityMember"/>
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    <link:label id="lab_us-gaap_DerivativeGainOnDerivative_2ac9ba78-a05c-4d7b-ac14-35f3e3238824_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainOnDerivative" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Gain on change in fair value</link:label>
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    <link:label id="lab_tlsi_WarrantsLiabilitiesTextBlock_f39c68dd-85c7-43da-bf29-7645a18accdc_terseLabel_en-US" xlink:label="lab_tlsi_WarrantsLiabilitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrants</link:label>
    <link:label id="lab_tlsi_WarrantsLiabilitiesTextBlock_label_en-US" xlink:label="lab_tlsi_WarrantsLiabilitiesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Warrants Liabilities [Text Block]</link:label>
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    <link:label id="lab_tlsi_PaymentsForAssetsAcquisitionMilestone_fa0bd8a1-04cc-4c11-8311-04b1a64d8600_negatedTerseLabel_en-US" xlink:label="lab_tlsi_PaymentsForAssetsAcquisitionMilestone" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xmlns:xml="http://www.w3.org/XML/1998/namespace" xml:lang="en-US">Milestone payments to Dynavax</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PaymentsForAssetsAcquisitionMilestone" xlink:href="tlsi-20230930.xsd#tlsi_PaymentsForAssetsAcquisitionMilestone"/>
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