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    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpensePolicy_507d5409-0254-4050-9a9a-637af5232a79_terseLabel_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Research and Development</link:label>
    <link:label id="lab_us-gaap_ResearchAndDevelopmentExpensePolicy_label_en-US" xlink:label="lab_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Research and Development Expense, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ResearchAndDevelopmentExpensePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:to="lab_us-gaap_ResearchAndDevelopmentExpensePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ProceedsFromReverseRecapitalizationTransaction_d4eb7f87-3cd0-4bbf-a378-0d40749a4716_totalLabel_en-US" xlink:label="lab_tlsi_ProceedsFromReverseRecapitalizationTransaction" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Proceeds From Reverse Recapitalization Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ProceedsFromReverseRecapitalizationTransaction" xlink:href="tlsi-20240331.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_NatureOfBusinessLineItems_7e8014cc-8a2e-4d48-b300-9277790d2f32_terseLabel_en-US" xlink:label="lab_tlsi_NatureOfBusinessLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Nature of Business [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_NatureOfBusinessLineItems" xlink:href="tlsi-20240331.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_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued_0ee9b58b-d62b-4631-9685-292ae240d6fa_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted stock units issued (in shares)</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Non-Options Equity Instruments, Issued</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Non-Options Equity Instruments, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:href="tlsi-20240331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionsEquityInstrumentsIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ScheduleOfReverseRecapitalizationTable_98955bd0-18f0-46f0-83ec-11f0db6b8673_terseLabel_en-US" xlink:label="lab_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Schedule of Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ScheduleOfReverseRecapitalizationTable" xlink:href="tlsi-20240331.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_tlsi_WarrantsIssuedInConnectionWithIssuanceOfPreferredStockValue_51ef5fe9-8b76-4a18-a464-d0f0ad20a2bd_terseLabel_en-US" xlink:label="lab_tlsi_WarrantsIssuedInConnectionWithIssuanceOfPreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Value of warrants issued with Series&#160;B-2 preferred stock</link:label>
    <link:label id="lab_tlsi_WarrantsIssuedInConnectionWithIssuanceOfPreferredStockValue_label_en-US" xlink:label="lab_tlsi_WarrantsIssuedInConnectionWithIssuanceOfPreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Warrants Issued In Connection With Issuance Of Preferred Stock, Value</link:label>
    <link:label id="lab_tlsi_WarrantsIssuedInConnectionWithIssuanceOfPreferredStockValue_documentation_en-US" xlink:label="lab_tlsi_WarrantsIssuedInConnectionWithIssuanceOfPreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Warrants Issued In Connection With Issuance Of Preferred Stock, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_WarrantsIssuedInConnectionWithIssuanceOfPreferredStockValue" xlink:href="tlsi-20240331.xsd#tlsi_WarrantsIssuedInConnectionWithIssuanceOfPreferredStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_WarrantsIssuedInConnectionWithIssuanceOfPreferredStockValue" xlink:to="lab_tlsi_WarrantsIssuedInConnectionWithIssuanceOfPreferredStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputPriceVolatilityMember_5c04a2c8-bb55-45a7-88d8-78f897208a45_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputPriceVolatilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_tlsi_AccruedClinicalTrialLiabilityCurrent_60ea5c6a-d25c-443c-b638-fa9600e0e6c6_terseLabel_en-US" xlink:label="lab_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued liabilities - clinical trials</link:label>
    <link:label id="lab_tlsi_AccruedClinicalTrialLiabilityCurrent_label_en-US" xlink:label="lab_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Clinical Trial Liability, Current</link:label>
    <link:label id="lab_tlsi_AccruedClinicalTrialLiabilityCurrent_documentation_en-US" xlink:label="lab_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Accrued Clinical Trial Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:href="tlsi-20240331.xsd#tlsi_AccruedClinicalTrialLiabilityCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:to="lab_tlsi_AccruedClinicalTrialLiabilityCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LoanFacilityInitialCommitmentAmountMember_0f489c82-18c4-4ed6-a57a-e070780a5ca9_terseLabel_en-US" xlink:label="lab_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Facility, Initial Commitment Amount</link:label>
    <link:label id="lab_tlsi_LoanFacilityInitialCommitmentAmountMember_label_en-US" xlink:label="lab_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Facility, Initial Commitment Amount [Member]</link:label>
    <link:label id="lab_tlsi_LoanFacilityInitialCommitmentAmountMember_documentation_en-US" xlink:label="lab_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Facility, Initial Commitment Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:href="tlsi-20240331.xsd#tlsi_LoanFacilityInitialCommitmentAmountMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:to="lab_tlsi_LoanFacilityInitialCommitmentAmountMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfWarrants_a1aad825-9880-40f7-ab2b-e271aa5237c0_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfWarrants" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_us-gaap_ProceedsFromIssuanceOfCommonStock_7ff53ca3-a493-4e59-b507-eba83a3d12a8_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from the issuance of common stock</link:label>
    <link:label id="lab_us-gaap_ProceedsFromIssuanceOfCommonStock_label_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Issuance of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ProceedsFromIssuanceOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:to="lab_us-gaap_ProceedsFromIssuanceOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume_ece1cde9-4397-4241-96c5-18b552813fd1_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockSharePricePercentageOfAverageDailyVolume" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_225a3047-31b7-4af4-8c4d-16655f7e0273_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_SPACWarrantsMember_165f5256-2b08-4f8f-949c-894e7fc9ccd4_terseLabel_en-US" xlink:label="lab_tlsi_SPACWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SPAC Warrants</link:label>
    <link:label id="lab_tlsi_SPACWarrantsMember_label_en-US" xlink:label="lab_tlsi_SPACWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">SPAC Warrants [Member]</link:label>
    <link:label id="lab_tlsi_SPACWarrantsMember_documentation_en-US" xlink:label="lab_tlsi_SPACWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">SPAC Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SPACWarrantsMember" xlink:href="tlsi-20240331.xsd#tlsi_SPACWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_SPACWarrantsMember" xlink:to="lab_tlsi_SPACWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesCurrentAbstract_7b21e634-4653-4d07-aecd-f16797194f6e_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_dff315da-6afe-4903-b69e-2c6d472e068c_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_bad52752-2ff3-44a0-957b-f343c1c1e1e9_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, Series A, $0.0001 par value per share, $10.00 liquidation value per share. Authorized $10,000,000 shares at March&#160;31, 2024 and December&#160;31, 2023, respectively; issued and outstanding, $4,015,002 shares at March&#160;31, 2024 and December&#160;31, 2023, 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" 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_dc49c0b6-d8c1-4e5a-8a3d-ca9ac0c9b38c_terseLabel_en-US" xlink:label="lab_tlsi_PaymentsForAssetAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Payments for Asset Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PaymentsForAssetAcquisition" xlink:href="tlsi-20240331.xsd#tlsi_PaymentsForAssetAcquisition"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PaymentsForAssetAcquisition" xlink:to="lab_tlsi_PaymentsForAssetAcquisition" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SubsequentEventTypeDomain_698cae82-3c88-4722-b452-54ff07632b11_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_e66afc04-1b6a-4ce0-814a-a9f65ce77e32_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:to="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_8263cd44-fa21-4286-aaed-59ca24c8deb8_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossLineItems_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeInstrumentsGainLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:to="lab_us-gaap_DerivativeInstrumentsGainLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockIssuedPricePerShare_4ab86d9b-330f-484f-83b6-3d33357c76d9_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Original issue price (in dollars per share)</link:label>
    <link:label id="lab_tlsi_PreferredStockIssuedPricePerShare_label_en-US" xlink:label="lab_tlsi_PreferredStockIssuedPricePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Issued Price Per Share</link:label>
    <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" 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-20240331.xsd#tlsi_PreferredStockIssuedPricePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockIssuedPricePerShare" xlink:to="lab_tlsi_PreferredStockIssuedPricePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_3f5df630-125c-45f9-88ca-ec9126d3bf50_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_e3f512db-4330-4421-8ae8-257468594ed4_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_aa3cdb10-e768-49f3-a337-8dcf98a57bf0_terseLabel_en-US" xlink:label="lab_us-gaap_AccountsReceivableNetCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" xml:lang="en-US">Accounts Receivable, after Allowance for Credit Loss, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountsReceivableNetCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccountsReceivableNetCurrent"/>
    <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_9f0c7789-2c18-4a90-973c-a917d676af17_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum shares of common stock allowed under Purchase Agreement (in shares)</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized_label_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAmountOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement, Maximum Amount Of Shares Authorized</link:label>
    <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" 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-20240331.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_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_fe5e5aaa-56f3-4e11-8b91-dff23946b0af_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock options outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract_994c8918-ed0b-4092-95fb-5b37fb24a87f_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other income (expense):</link:label>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Nonoperating Income (Expense) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherNonoperatingIncomeExpenseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:to="lab_us-gaap_OtherNonoperatingIncomeExpenseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_c5b9ac60-fcf4-42a9-83d5-04140b6ee7ce_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" xml:lang="en-US">Stock Issued During Period, Value, Stock Options Exercised</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_b8306c4c-c058-4a23-980b-617732f52cb7_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_3c11f30c-f5ea-4173-ad99-de2aab30a9ee_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options, weighted average fair value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Weighted Average Grant Date Fair Value</link:label>
    <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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLoss_4db926fb-09e1-45ec-b95e-4c6b8970b78e_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss available to common stockholders</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_6d15e826-1fcd-48f8-8bd5-eaed20145f48_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_e2ee830f-2c6a-4ae5-84e6-ef6f472dc55c_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" 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" xml:lang="en-US">Net Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetIncomeLoss"/>
    <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_5fd8023e-993c-4e0a-b046-1c318e580011_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" 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" 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_DerivativeContractTypeDomain_899fce6a-c03c-40c8-9c5a-87cd43cc2f0d_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:label id="lab_us-gaap_DerivativeContractTypeDomain_label_en-US" xlink:label="lab_us-gaap_DerivativeContractTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Contract [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeContractTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeContractTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeContractTypeDomain" xlink:to="lab_us-gaap_DerivativeContractTypeDomain" 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" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice_2a5448fc-66fc-4083-91a2-bb65ca4efd96_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of warrant or right, redemption price (in dollars per share)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Redemption Price</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class of Warrant or Right, Redemption Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:href="tlsi-20240331.xsd#tlsi_ClassOfWarrantOrRightRedemptionPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:to="lab_tlsi_ClassOfWarrantOrRightRedemptionPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable_cb94501d-763c-4110-84d1-71bbb2e591cb_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Standards Update and Change in Accounting Principle [Table]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:to="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_0b52a702-b7ec-43e8-a415-f86b9e3f5535_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cash and Cash Equivalents</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Cash and Cash Equivalents [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ScheduleOfCashAndCashEquivalentsTableTextBlock"/>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_3c7e778d-2905-41a3-a97d-1b5a81347801_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities and Stockholders&#8217; Deficit</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LiabilitiesAndStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:to="lab_us-gaap_LiabilitiesAndStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityExTransitionPeriod_56dc5f4f-869b-4a4f-bddc-daee26b9adc1_terseLabel_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:label id="lab_dei_EntityExTransitionPeriod_label_en-US" xlink:label="lab_dei_EntityExTransitionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Ex Transition Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityExTransitionPeriod" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityExTransitionPeriod"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_5d422e01-4979-4f92-8e3e-e654b2ce3f11_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockMember_2f194396-adb5-4dc4-be3e-974dd8a5386d_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee Stock</link:label>
    <link:label id="lab_us-gaap_EmployeeStockMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EmployeeStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockMember" xlink:to="lab_us-gaap_EmployeeStockMember" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable_label_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instruments, Gain (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DerivativeInstrumentsGainLossByHedgingRelationshipByIncomeStatementLocationByDerivativeInstrumentRiskTable"/>
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    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_fcc85513-37b2-4313-ad26-ee577cee1dd1_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise of options (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_560e6e55-0f7b-446e-8303-8fc6cac46a24_terseLabel_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost of goods sold</link:label>
    <link:label id="lab_us-gaap_CostOfGoodsAndServicesSold_label_en-US" xlink:label="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cost of Goods and Services Sold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CostOfGoodsAndServicesSold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CostOfGoodsAndServicesSold" xlink:to="lab_us-gaap_CostOfGoodsAndServicesSold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_64973b1c-12ab-46d0-ab86-2d93d324c9c4_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based payment arrangement, contractual term</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Award Vesting Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock_88966169-9c67-48cf-bec4-76b000d648bf_terseLabel_en-US" xlink:label="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Plan Balances</link:label>
    <link:label id="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock_label_en-US" xlink:label="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disclosure of Share-Based Compensation Arrangements by Share-Based Payment Award [Table 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_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:to="lab_us-gaap_DisclosureOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_6a64cfce-cf9d-46f4-ae59-47580d22f623_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements or Change in Accounting Principle [Line Items]</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements or Change in Accounting Principle [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:to="lab_us-gaap_NewAccountingPronouncementsOrChangeInAccountingPrincipleLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockConversionPriceFloor_e2d9e3bf-47fa-4bd1-a49c-87b1cbcbaf5e_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceFloor" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series A Convertible Preferred Stock, floor conversion price (in dollars per share)</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceFloor_label_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceFloor" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Conversion Price, Floor</link:label>
    <link:label id="lab_tlsi_PreferredStockConversionPriceFloor_documentation_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceFloor" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock, Conversion Price, Floor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockConversionPriceFloor" xlink:href="tlsi-20240331.xsd#tlsi_PreferredStockConversionPriceFloor"/>
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    <link:label id="lab_tlsi_DerivativeInstrumentPeriodTwoMember_556738a4-e2b6-45d7-b14c-c0ee425db2d5_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tranche Two</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodTwoMember_label_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period Two [Member]</link:label>
    <link:label id="lab_tlsi_DerivativeInstrumentPeriodTwoMember_documentation_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodTwoMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Derivative Instrument, Period Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodTwoMember" xlink:href="tlsi-20240331.xsd#tlsi_DerivativeInstrumentPeriodTwoMember"/>
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    <link:label id="lab_tlsi_ClassOfWarrantsOrRightsIssuedInThePeriod_d95d956f-2486-4007-81d3-1e716ddd8e18_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantsOrRightsIssuedInThePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants issued in the period (in shares)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantsOrRightsIssuedInThePeriod_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantsOrRightsIssuedInThePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrants Or Rights Issued In The Period</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantsOrRightsIssuedInThePeriod" xlink:href="tlsi-20240331.xsd#tlsi_ClassOfWarrantsOrRightsIssuedInThePeriod"/>
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    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_f3388e4e-0aab-403a-a82a-8fdcf6ac401c_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary Of Significant Accounting Policies</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_b5345640-1f20-4b43-8e29-804f686bbba1_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">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" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
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    <link:label id="lab_us-gaap_PatentsMember_3c1f03c6-89a7-4f5f-8c01-df89535c6590_terseLabel_en-US" xlink:label="lab_us-gaap_PatentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Patents</link:label>
    <link:label id="lab_us-gaap_PatentsMember_label_en-US" xlink:label="lab_us-gaap_PatentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Patents [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PatentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PatentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PatentsMember" xlink:to="lab_us-gaap_PatentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_d27cdd3f-09fb-4583-85fb-2626f66a4895_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_df398501-a8ac-441c-8c1a-501961989b76_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_f8dec76d-613a-45b8-87a9-f2d99bf55b62_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_f63dffaf-9cff-4489-b32f-1154906bd3d9_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_862dc049-86ae-4854-a5f8-a70fd839c545_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_6fe8369f-11e1-4088-9d47-8645f884c23a_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_44508582-a021-47ef-93bb-cc1014b57a46_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_a908da6c-8f5e-409d-9c63-23268a6eff13_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_db7bd852-8d7b-42e9-a123-aa373a0eda6c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" 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" 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_c01a7418-3b15-413e-a3ff-7bc748b4acd3_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilitySettlements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_c2ab53a4-0083-4eab-8453-7a52d72a1d2a_terseLabel_en-US" xlink:label="lab_tlsi_MedTechAcquisitionCorporationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">MedTech Acquisition Corporation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_MedTechAcquisitionCorporationMember" xlink:href="tlsi-20240331.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_834e82e5-f819-4338-acb9-c05699b54d8c_verboseLabel_en-US" xlink:label="lab_tlsi_PaymentsOfReverseRecapitalizationTransactionCosts" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" 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" 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" 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-20240331.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_ea59a452-63c0-484f-be85-664d6132c58b_terseLabel_en-US" xlink:label="lab_us-gaap_WarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_ClassOfWarrantOrRightConversionDaysNotice_b368367b-8aab-48e2-b6c4-2d0e9e1865d3_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" xml:lang="en-US">Class Of Warrant Or Right, Conversion Days Notice</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Conversion Days Notice</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:href="tlsi-20240331.xsd#tlsi_ClassOfWarrantOrRightConversionDaysNotice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:to="lab_tlsi_ClassOfWarrantOrRightConversionDaysNotice" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PrivateWarrantsMember_863308b1-3933-4482-bda2-d80419049497_terseLabel_en-US" xlink:label="lab_tlsi_PrivateWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Private Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PrivateWarrantsMember" xlink:href="tlsi-20240331.xsd#tlsi_PrivateWarrantsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PrivateWarrantsMember" xlink:to="lab_tlsi_PrivateWarrantsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_6da80ad5-78cd-4111-a7c0-558219a88e84_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockUnitsRSUMember" xlink:to="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_NatureOfBusinessTable_46f2710f-0fd1-4dcb-83d1-8be3b7fef37e_terseLabel_en-US" xlink:label="lab_tlsi_NatureOfBusinessTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Nature of Business [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_NatureOfBusinessTable" xlink:href="tlsi-20240331.xsd#tlsi_NatureOfBusinessTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_NatureOfBusinessTable" xlink:to="lab_tlsi_NatureOfBusinessTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfWarrantOrRightTable_666ac33f-e27f-4e26-93f3-9cf886072fde_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_DebtInstrumentNameDomain_fcc406a9-b7ba-4a63-92cf-a0e1772e36f0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
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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" 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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityDisclosureAbstract" xlink:to="lab_us-gaap_TemporaryEquityDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends_470080b9-1023-4191-9b82-5ee4932701df_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Undeclared cumulative dividends</link:label>
    <link:label id="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends_label_en-US" xlink:label="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock Dividends, Undeclared Cumulative Dividends</link:label>
    <link:label id="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends_documentation_en-US" xlink:label="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Preferred Stock Dividends, Undeclared Cumulative Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:href="tlsi-20240331.xsd#tlsi_PreferredStockDividendsUndeclaredCumulativeDividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:to="lab_tlsi_PreferredStockDividendsUndeclaredCumulativeDividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_1cfdd4e8-3641-4d5b-918c-fcf1ce0a68b4_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of stock (in shares)</link:label>
    <link:label id="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction_label_en-US" xlink:label="lab_us-gaap_SaleOfStockNumberOfSharesIssuedInTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock, Number of Shares Issued in Transaction</link:label>
    <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_AccruedIncomeTaxesCurrent_0a4a3f94-e9a6-456a-aae1-0cca09ec3137_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued taxes</link:label>
    <link:label id="lab_us-gaap_AccruedIncomeTaxesCurrent_label_en-US" xlink:label="lab_us-gaap_AccruedIncomeTaxesCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Income Taxes, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedIncomeTaxesCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AccruedIncomeTaxesCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedIncomeTaxesCurrent" xlink:to="lab_us-gaap_AccruedIncomeTaxesCurrent" 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" 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_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement_e5238ec1-c129-4687-bd00-618f9143d9b1_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares authorized, standby equity purchase agreement (in shares)</link:label>
    <link:label id="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement_label_en-US" xlink:label="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized, Standby Equity Purchase Agreement</link:label>
    <link:label id="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement_documentation_en-US" xlink:label="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized, Standby Equity Purchase Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:href="tlsi-20240331.xsd#tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:to="lab_tlsi_CommonStockSharesAuthorizedStandbyEquityPurchaseAgreement" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember_e250bce3-2d28-4baa-9f94-09f402f9d382_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputRiskFreeInterestRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_66c1f578-2ab1-49d2-a741-16a38fece321_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationByLiabilityClassDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_TemporaryEquityCarryingAmountAttributableToParent_d22008bf-b81a-4ff0-9f58-245a2a535403_periodStartLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Convertible preferred stock, beginning balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_f496e131-26cf-4fb4-985a-105e2003ce7f_periodEndLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Convertible preferred stock, ending balance</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, Carrying Amount, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_TemporaryEquityCarryingAmountAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:to="lab_us-gaap_TemporaryEquityCarryingAmountAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ContingentEarnoutLiabilityMember_18fd6b71-ee10-4d23-9289-192047983670_terseLabel_en-US" xlink:label="lab_tlsi_ContingentEarnoutLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Contingent Earnout Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ContingentEarnoutLiabilityMember" xlink:href="tlsi-20240331.xsd#tlsi_ContingentEarnoutLiabilityMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_e9e32217-4f1c-42ca-90d8-e0d58eb9dc79_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share</link:label>
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    <link:label id="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays_25a6b273-b9a1-4ec3-8ca6-85e67761ed06_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of warrant or right, conversion terms, threshold consecutive trading days</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays" xlink:href="tlsi-20240331.xsd#tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays" xlink:to="lab_tlsi_ClassOfWarrantOrRightConversionTermsThresholdConsecutiveTradingDays" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInInventories_23ef6e42-7b0b-4ea4-b7e0-bce595ef40c7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInInventories" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Inventory, net</link:label>
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    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued_d47f7ff6-2d9c-4960-a760-7bbc79965fd4_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock options issued (in shares)</link:label>
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    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Issued</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance_2fd7e92f-5e38-4e75-a69b-fd4344f7123a_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockPeriodIncreaseDecreaseInCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in common stock reserve for future issuance (in shares)</link:label>
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    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_0092b279-dc10-4733-95f5-5c4e9c3a7ff0_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recently Adopted Accounting Pronouncements and Accounting Pronouncements Not Yet Adopted</link:label>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_05dd6fb5-3839-4220-b3c6-27703bdd08ab_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, cash equivalents and restricted cash, beginning of period</link:label>
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    <link:label id="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction_b0f59ea7-9c23-4614-a4a6-17cd606f8e19_terseLabel_en-US" xlink:label="lab_us-gaap_SaleOfStockConsiderationReceivedOnTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of common stock</link:label>
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    <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_us-gaap_EmployeeStockOptionMember_88af639d-e214-4521-8738-21ee5c3c26b2_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_6942fcdd-cf48-4951-bc02-c114a2ffdb37_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent Earnout Liability</link:label>
    <link:label id="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock_f4076a9c-5646-4c43-9432-e3b40a6c4a15_verboseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement</link:label>
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    <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"/>
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    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfTotalShares_f4a3e4ef-4009-44e6-8bb9-9caf26f4eed9_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfTotalShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation arrangement by share-based payment award, automatic increase, percentage of total shares</link:label>
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    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfTotalShares_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfTotalShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-based Payment Award, Automatic Increase, Percentage of Total Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfTotalShares" xlink:href="tlsi-20240331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfTotalShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfTotalShares" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePercentageOfTotalShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1_9cc1d0b9-4602-47b4-864d-4a591cbf2389_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation expense, recognition period</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognizedPeriodForRecognition1"/>
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    <link:label id="lab_us-gaap_AssetAcquisitionTable_4cb18830-ea0a-4221-af0f-3338047aac66_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_67ba5a26-16c2-453f-b711-c5c58780c152_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_32e549eb-531c-4f14-8430-b1198971607c_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized compensation expense</link:label>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_label_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized"/>
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    <link:label id="lab_dei_DocumentType_88e62817-9a7a-415f-a5c8-ac7e7c3d1d7e_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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"/>
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    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember_4269810e-687c-4167-88f7-559c8bbcdea6_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Derivative Financial Instruments, Warrant Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeFinancialInstrumentsWarrantLiabilityMember" xlink:href="tlsi-20240331.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_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber_1c4d5468-76fe-48c9-abc5-e0e3c10fab5a_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted stock units outstanding (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNonOptionEquityInstrumentsOutstandingNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsSharesReturnedFromOptionsExercisedCorrectionOfClericalError_1b8b495b-3a1c-4fe2-9698-56f10d819e80_negatedTerseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsSharesReturnedFromOptionsExercisedCorrectionOfClericalError" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares returned from options exercised, correction of clerical error (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsSharesReturnedFromOptionsExercisedCorrectionOfClericalError" xlink:href="tlsi-20240331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsSharesReturnedFromOptionsExercisedCorrectionOfClericalError"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsSharesReturnedFromOptionsExercisedCorrectionOfClericalError" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsSharesReturnedFromOptionsExercisedCorrectionOfClericalError" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_1ad8c24f-b9ae-41d0-b99f-f8505342a9e3_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
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    <link:label id="lab_tlsi_RecapitalizationExchangeRatio_cb3a6497-0bb0-43a9-be42-f5a839b863c6_terseLabel_en-US" xlink:label="lab_tlsi_RecapitalizationExchangeRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exchange ratio (in shares)</link:label>
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    <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" xml:lang="en-US">Recapitalization Exchange Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_RecapitalizationExchangeRatio" xlink:href="tlsi-20240331.xsd#tlsi_RecapitalizationExchangeRatio"/>
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    <link:label id="lab_us-gaap_AssetAcquisitionTextBlock_d04c009b-d638-4c3c-aa9b-d0ea1f25e050_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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"/>
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    <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"/>
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    <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_cda3b4cf-dfba-4685-84dd-44788d7b57fa_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromContributedCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_407122ed-33a4-47d5-ba46-2636de97c6ca_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_6bf7217a-9b17-4c3c-9a36-758e38e734fa_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputSharePriceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_910f52d9-2305-4794-ad25-7086e0501dee_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_cef17453-b647-45ca-9115-3ff94c6aeb28_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityTransfersNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_1a3c0893-a153-493c-a380-108af0a0a9d9_terseLabel_en-US" xlink:label="lab_tlsi_NumberOfProductLinesInDevelopment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_290d3b22-d187-4c14-a4e2-a20eca5d4261_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_a17c861e-a92b-4436-9761-612425d8fbbf_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_26dc8fcc-102c-4aab-a378-4362371f94f0_terseLabel_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities_e5401d8e-7754-4eea-be96-e0ac7844e60b_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccountsPayableAndAccruedLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trade payables and accrued 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" 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" 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_c1ee7734-9bc8-4d08-92ce-9a0e84961fac_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryRawMaterialsNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_d9846eac-26e3-4e96-84d6-c340ca43c6a1_terseLabel_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationLineItems" xlink:href="tlsi-20240331.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_us-gaap_StockIssuedDuringPeriodSharesNewIssues_2f607ce1-525d-43e6-a79c-f3533d5fe4af_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of common stock (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues_3462d06b-c8f4-40e9-8411-7c375fc54e97_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_6a49b39f-410a-45f4-8321-60f02c631186_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays_4138999c-83a1-43f4-9978-57c501e541cf_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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" 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_3794b045-df84-4364-b09b-ab48f05b190f_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePerYearNumberOfYears" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_0c47df9a-5a8f-4e12-b263-c74b7bc87933_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_c8721a9a-9399-48f5-8f8e-aa14f95991c3_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_PreferredStockConvertibleDownRoundFeatureIncreaseDecreaseInEquityAmount1_f52d7a95-bd08-4715-853d-76b72032bfa9_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockConvertibleDownRoundFeatureIncreaseDecreaseInEquityAmount1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_e061b185-74fa-41b3-9741-eb3f5056f67e_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionRoyaltyPercentageOverThresholdAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_432648d3-449a-4736-8944-f0169f49f4fe_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockAutomaticConversionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Preferred Stock, Automatic Conversion, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockAutomaticConversionPeriod" xlink:href="tlsi-20240331.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" 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_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_label_en-US" xlink:label="lab_us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" 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_dei_EntityTaxIdentificationNumber_01c9786f-5d84-475b-85b6-d288fc468651_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_6b651f42-8a9a-42be-854b-3f8c6cdb459a_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Asset Acquisition, Maximum Milestone Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionMaximumMilestoneAmount" xlink:href="tlsi-20240331.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_us-gaap_InventoryNet_fd37cce6-9103-4bda-bb2e-08dea9e22b0e_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Inventory, net</link:label>
    <link:label id="lab_us-gaap_InventoryNet_8ecd5726-ee82-4641-a14c-24bec578232c_totalLabel_en-US" xlink:label="lab_us-gaap_InventoryNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" 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" 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_us-gaap_ProceedsFromIssuanceOfPrivatePlacement_058c9271-86fd-4831-b2d0-50e95a384260_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfPrivatePlacement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_471a4e76-a03a-49b7-925a-368665e4c7b5_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_edecb804-4170-4e04-b2e2-c81ed847d62c_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_dei_EntityCommonStockSharesOutstanding_df125f6e-db1a-401c-873c-ab5c86a757b1_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_e02184ba-8ab2-48e7-b3e7-095a706c3b2e_terseLabel_en-US" xlink:label="lab_us-gaap_CashFlowNoncashInvestingAndFinancingActivitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental disclosures of cash flow information:</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" 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" 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_4210aec0-7073-4e9b-9433-1ded7751dc6f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_09ff666a-101b-4c88-b2af-0f8ae27aca59_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_7343b0d3-02f9-4eb4-a4dc-c0427e841cb4_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_c57fc773-75c5-404a-abfb-a94bb03a5e34_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated deficit</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_20049914-52b2-45fd-be9b-906cbb96c374_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" 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" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
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    <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" 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"/>
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    <link:label id="lab_dei_EntityIncorporationStateCountryCode_b4e2fe2f-5937-4159-8158-23cd12ea825a_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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"/>
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    <link:label id="lab_us-gaap_AssetsCurrentAbstract_ab46ba06-52d5-4090-aa28-e3f217084a5b_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrentAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_9ee86771-280d-4012-8838-3c971cf2db61_terseLabel_en-US" xlink:label="lab_tlsi_DynavaxTechnologiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Dynavax Technologies</link:label>
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    <link:label id="lab_dei_EntityAddressStateOrProvince_249e28c1-8d81-4576-86aa-bf6d0e93a593_terseLabel_en-US" xlink:label="lab_dei_EntityAddressStateOrProvince" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_81545a29-d854-44bc-9725-41fc75256ae7_terseLabel_en-US" xlink:label="lab_srt_CounterpartyNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember_c8a26569-5da1-4479-8149-8df2e9efb22b_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">SEPA derivative liability</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember_label_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement (SEPA) Derivative Liability [Member]</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember_documentation_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement (SEPA) Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:href="tlsi-20240331.xsd#tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:to="lab_tlsi_StandbyEquityPurchaseAgreementSEPADerivativeLiabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativesPolicyTextBlock_137ba030-c21a-4df4-88e8-6b2d38c19b86_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativesPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant Liabilities, Contingent Earnout Liability, Standby Equity Purchase Agreement</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" 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_0db6a9ab-71ab-4fc4-bcbe-096a84b6873b_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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"/>
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    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_c535ea75-889b-425c-ace2-3393e19470b0_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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"/>
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    <link:label id="lab_us-gaap_ClassOfWarrantOrRightDomain_d393440c-03cd-48e0-b82b-035d37730c3b_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" xml:lang="en-US">Class of Warrant or Right [Domain]</link:label>
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    <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_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_80a3a585-6d7a-4170-b037-8260186f18f1_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ReverseRecapitalizationTransactionCostsIncurred_253fe8bc-42d5-4424-ad12-af2d344f9eab_terseLabel_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationTransactionCostsIncurred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Transaction costs incurred</link:label>
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    <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" xml:lang="en-US">Reverse Recapitalization, Transaction Costs Incurred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationTransactionCostsIncurred" xlink:href="tlsi-20240331.xsd#tlsi_ReverseRecapitalizationTransactionCostsIncurred"/>
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    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_98b0bbef-e1d9-4502-a198-727051dd4fa3_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, shares outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_faac4dea-e271-411f-b70f-785d2b6b7185_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balances, beginning of period (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_2fad6a1a-2a1a-44d6-8372-101e00c6e902_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Balances, end of period (in shares)</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearFour_5cf8aedd-78fd-43fb-9466-32af944eeed2_terseLabel_en-US" xlink:label="lab_tlsi_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
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    <link:label id="lab_tlsi_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearFour_documentation_en-US" xlink:label="lab_tlsi_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearFour" xlink:href="tlsi-20240331.xsd#tlsi_FiniteLivedIntangibleAssetExpectedAmortizationAfterYearFour"/>
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    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_c96fe69e-c478-4bc7-9dc9-21a9bd735987_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
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    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_4c830359-7823-4274-81cd-0c8d9f0f58a5_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <link:label id="lab_us-gaap_SubsidiarySaleOfStockAxis_label_en-US" xlink:label="lab_us-gaap_SubsidiarySaleOfStockAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Sale of Stock [Axis]</link:label>
    <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_3e664116-ce64-4a39-b177-8102b97254ca_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in investing activities</link:label>
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    <link:label id="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_425029cd-34f0-4cf8-9385-d802024e5aa6_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockCapitalSharesReservedForFutureIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock reserved for future issuance (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SellingAndMarketingExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SellingAndMarketingExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SellingAndMarketingExpense" xlink:to="lab_us-gaap_SellingAndMarketingExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_0679447f-f50c-4e5d-bb7c-5f0e756f31b5_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock, $0.0001 par value per share. Authorized $400,000,000 shares at March&#160;31, 2024 and December&#160;31, 2023, respectively; issued and outstanding, 26,758,272 and $26,413,213 shares at March 31, 2024, and December&#160;31, 2023, 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" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TemporaryEquityByClassOfStockTable_825addf0-9c0e-40a0-bcaa-e0c0068d6bae_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Temporary Equity, by Class of Stock [Table]</link:label>
    <link:label id="lab_us-gaap_TemporaryEquityByClassOfStockTable_label_en-US" xlink:label="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Temporary Equity, by Class of Stock [Table]</link:label>
    <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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TemporaryEquityByClassOfStockTable" xlink:to="lab_us-gaap_TemporaryEquityByClassOfStockTable" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_MeasurementInputExpectedDrawsMember_ad37ffca-843d-44a9-905f-8cb2835a1bf7_terseLabel_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedDrawsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected draws</link:label>
    <link:label id="lab_tlsi_MeasurementInputExpectedDrawsMember_label_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedDrawsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Draws [Member]</link:label>
    <link:label id="lab_tlsi_MeasurementInputExpectedDrawsMember_documentation_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedDrawsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Draws</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_MeasurementInputExpectedDrawsMember" xlink:href="tlsi-20240331.xsd#tlsi_MeasurementInputExpectedDrawsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_MeasurementInputExpectedDrawsMember" xlink:to="lab_tlsi_MeasurementInputExpectedDrawsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_febda309-2e9e-4847-83fe-1bd68163796a_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <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_10cd40a1-d9bb-4c37-ac56-e4cc4191c362_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightNumberOfWarrantsRepurchased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrants repurchased (in shares)</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightNumberOfWarrantsRepurchased_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightNumberOfWarrantsRepurchased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Number Of Warrants Repurchased</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightNumberOfWarrantsRepurchased_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightNumberOfWarrantsRepurchased" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Number Of Warrants Repurchased</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightNumberOfWarrantsRepurchased" xlink:href="tlsi-20240331.xsd#tlsi_ClassOfWarrantOrRightNumberOfWarrantsRepurchased"/>
    <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" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_a3ad0bd5-7319-4a8c-80da-610b6e841721_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reduction in the carrying amount of right-of-use assets</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Periodic Reduction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAssetAmortizationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsCurrent_400d7ed7-5cbb-4eb9-bc47-a1be5065fff1_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current assets</link:label>
    <link:label id="lab_us-gaap_AssetsCurrent_label_en-US" xlink:label="lab_us-gaap_AssetsCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AssetsCurrent"/>
    <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_5ef725db-3ef8-4104-a8cf-19d085ae9716_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_ad7ef8a6-f1d3-4939-b552-ead149a745ef_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FinanceLeasePrincipalPayments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" 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" 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_tlsi_NumberOfEquityIncentivePlans_fbb8051e-d291-44c7-a96c-60d659ba7d92_terseLabel_en-US" xlink:label="lab_tlsi_NumberOfEquityIncentivePlans" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of equity incentive plans</link:label>
    <link:label id="lab_tlsi_NumberOfEquityIncentivePlans_label_en-US" xlink:label="lab_tlsi_NumberOfEquityIncentivePlans" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Equity Incentive Plans</link:label>
    <link:label id="lab_tlsi_NumberOfEquityIncentivePlans_documentation_en-US" xlink:label="lab_tlsi_NumberOfEquityIncentivePlans" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Equity Incentive Plans</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_NumberOfEquityIncentivePlans" xlink:href="tlsi-20240331.xsd#tlsi_NumberOfEquityIncentivePlans"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_NumberOfEquityIncentivePlans" xlink:to="lab_tlsi_NumberOfEquityIncentivePlans" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherNonoperatingIncomeExpense_e7fa4932-3427-44a1-9b6f-f33580c8f529_terseLabel_en-US" xlink:label="lab_us-gaap_OtherNonoperatingIncomeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_eaebf8e9-90bb-4aaf-b30b-8f62c3c4da4e_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_d315597e-c4b1-4b55-8194-aa11119dd93b_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationSecondReset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_ec9cce17-cd26-42bc-8b90-97d56572d958_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodVestingPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_a38d44cf-1ad2-4185-911d-5df4d89e6c16_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_d7611163-5a3d-4ff9-9c24-0b5d38b33fc2_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent earnout liability</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:to="lab_us-gaap_BusinessCombinationContingentConsiderationLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_0cb490f8-9d86-4bd7-a3a0-a95e6cba9f16_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_af99dbaf-2abe-4a70-83a8-56b9ff7a9b0d_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in operating activities</link:label>
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    <link:label id="lab_us-gaap_ProceedsFromWarrantExercises_132aeb71-06f5-4362-b4f7-eca9644bb1b6_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromWarrantExercises" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from exercise of preferred stock warrants</link:label>
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    <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" xml:lang="en-US">Business Combination and Asset Acquisition [Abstract]</link:label>
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    <link:label id="lab_us-gaap_StockholdersEquity_5bbca6fa-f33a-4784-a9ae-fd49a5bd6be0_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total stockholders&#8217; deficit</link:label>
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    <link:label id="lab_tlsi_CommonStockWarrantMember_aad31fd6-3b79-4c8f-aa16-753739f15874_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common stock warrants</link:label>
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    <link:label id="lab_us-gaap_PreferredStockSharesIssued_16c19165-1506-453d-9b0b-dd0db7aa9b98_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Preferred stock, shares issued (in shares)</link:label>
    <link:label id="lab_us-gaap_PreferredStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_PreferredStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock, Shares Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PreferredStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockSharesIssued" xlink:to="lab_us-gaap_PreferredStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_0c348f80-a6cd-4e41-8442-9bad9891e5b9_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_LeaseLiabilityNoncurrent_af8815d0-7273-452b-ad20-2794999a7f29_terseLabel_en-US" xlink:label="lab_tlsi_LeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term lease liabilities</link:label>
    <link:label id="lab_tlsi_LeaseLiabilityNoncurrent_label_en-US" xlink:label="lab_tlsi_LeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lease Liability, Noncurrent</link:label>
    <link:label id="lab_tlsi_LeaseLiabilityNoncurrent_documentation_en-US" xlink:label="lab_tlsi_LeaseLiabilityNoncurrent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lease Liability, Noncurrent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LeaseLiabilityNoncurrent" xlink:href="tlsi-20240331.xsd#tlsi_LeaseLiabilityNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LeaseLiabilityNoncurrent" xlink:to="lab_tlsi_LeaseLiabilityNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_f6ebd502-9b23-4ab5-80b3-91d013008c11_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_e6b7b16a-fcc0-4213-8178-9233efa38a7a_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Stockholders' Equity [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInStockholdersEquityRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:to="lab_us-gaap_IncreaseDecreaseInStockholdersEquityRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_a4d5e6c0-240c-4c7b-9206-e18821c771b0_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife_cd13ca46-5236-4986-bc50-2089bcb10087_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible asset, useful life</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StockConvertedReverseRecapitalization_04b7ac4d-7704-4e5a-9938-c55f265030ea_terseLabel_en-US" xlink:label="lab_tlsi_StockConvertedReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock converted, reverse recapitalization (in shares)</link:label>
    <link:label id="lab_tlsi_StockConvertedReverseRecapitalization_label_en-US" xlink:label="lab_tlsi_StockConvertedReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Converted, Reverse Recapitalization</link:label>
    <link:label id="lab_tlsi_StockConvertedReverseRecapitalization_documentation_en-US" xlink:label="lab_tlsi_StockConvertedReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Stock Converted, Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StockConvertedReverseRecapitalization" xlink:href="tlsi-20240331.xsd#tlsi_StockConvertedReverseRecapitalization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StockConvertedReverseRecapitalization" xlink:to="lab_tlsi_StockConvertedReverseRecapitalization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_fb1e9614-3b4f-450b-80c4-f492fac5fbd5_terseLabel_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:to="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock_c1cebd55-e0d4-4d4b-bb99-8ca1494bb631_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Standby equity purchase agreement, maximum allowable percentage of outstanding common stock</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock_label_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement, Maximum Allowable Percentage Of Outstanding Common Stock</link:label>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock_documentation_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standby Equity Purchase Agreement, Maximum Allowable Percentage Of Outstanding Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:href="tlsi-20240331.xsd#tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:to="lab_tlsi_StandbyEquityPurchaseAgreementMaximumAllowablePercentageOfOutstandingCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_7a78a85b-bc1b-4086-9cdd-a852f3d8d21e_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock-based compensation expense</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable_d896f81c-1fec-43ec-b6ed-c82165b20b06_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightThresholdNumberOfDaysForWarrantsToBeTransferable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_d2f2004f-192a-47b3-9466-fc6af51d9bca_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Common stock, $0.0001 par value</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_027d3f37-ffd3-44f0-ba0d-679aa63f21cd_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_5d02bc7e-be06-4152-a51e-7b3fd2dbe0a5_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromIssuanceOfConvertiblePreferredStock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_4e5e1243-2ec2-45f9-bb5b-da8e4bca916b_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_432fa109-cd4c-4268-8991-49a8bacf3b04_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_d7445ac8-e85b-4e24-bc0e-ba3b19c22a19_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod_f0a089f1-93ec-430b-8761-49c5186ed567_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation arrangement by share-based payment award, automatic increase period</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-based Payment Award, Automatic Increase Period</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-based Payment Award, Automatic Increase Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:href="tlsi-20240331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardAutomaticIncreasePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_ed72f7f6-5dd5-4114-9c16-abdd2ed178c8_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summary of Changes in Fair Value of Outstanding Warrant and Tranche Liabilities</link:label>
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    <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"/>
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    <link:label id="lab_dei_DocumentFiscalYearFocus_a1dd26e8-fcad-4704-b7b0-97a0a2cdbec7_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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"/>
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    <link:label id="lab_tlsi_DerivativeInstrumentPeriodFourMember_bc319418-540a-44eb-aad8-18c109babd5e_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodFourMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Derivative Instrument, Period Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodFourMember" xlink:href="tlsi-20240331.xsd#tlsi_DerivativeInstrumentPeriodFourMember"/>
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    <link:label id="lab_us-gaap_AccruedVacationCurrent_8cf2427f-4747-4685-8796-ffc1bd60a856_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedVacationCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_c9b742a8-f79d-4a8e-bc19-09b99ae0d499_terseLabel_en-US" xlink:label="lab_srt_MinimumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_0ea384e4-dcf5-4710-a28f-23ad4f24ab46_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_2c79feae-8770-4432-9ad8-736b8c684c59_terseLabel_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Reverse Recapitalization Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationDisclosureTextBlock" xlink:href="tlsi-20240331.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_FiniteLivedIntangibleAssetsByMajorClassAxis_84846c43-5378-4c31-ba4e-f9eec84af775_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets by Major Class [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock_fc2ccac1-f203-4cad-a56c-24cfff224ea7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockholdersEquityNoteWarrantsOrRightsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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_bf62ac57-c393-455e-8830-10c5e907fcd4_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_GoodwillAndIntangibleAssetsDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Goodwill and Intangible Assets Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:to="lab_us-gaap_GoodwillAndIntangibleAssetsDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability_55b7d5ce-76c8-49e5-bb59-fb7d3892060b_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease liabilities</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" xml:lang="en-US">Increase (Decrease) in Operating Lease Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IncreaseDecreaseInOperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract_c40262f1-bac4-48f9-89ad-38d3f69ad412_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesContinuingOperationsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss_f6d64633-222b-401d-81bc-530004682649_negatedLabel_en-US" xlink:label="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Change in Unrealized (Gains) Losses</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:to="lab_us-gaap_FairValueLiabilitiesMeasuredOnRecurringBasisChangeInUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_bf4a7bc2-6033-458f-a35b-5f1c465b9cb9_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by financing activities</link:label>
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    <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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock_ee4debc9-9ad5-4a75-9a47-63451a357cd0_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments And Contingencies</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsMember_8b3526d0-5a47-43bf-a44b-6c582b770e01_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" xml:lang="en-US">Retained Earnings [Member]</link:label>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_eae97030-4bbe-4483-8c23-2e9791077568_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities and stockholders&#8217; deficit</link:label>
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    <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_us-gaap_OtherLiabilitiesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Liabilities Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OtherLiabilitiesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:to="lab_us-gaap_OtherLiabilitiesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeInstrumentRiskAxis_3d794b99-2689-40f8-8a7b-49be2c4a8d79_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeInstrumentRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_4beb51f6-c1f0-4e16-a558-508f7794d5af_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net loss to net cash used in operating activities:</link:label>
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    <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"/>
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    <link:label id="lab_us-gaap_FairValueByLiabilityClassAxis_56604289-9d91-4fec-bb3e-eb81838ddfbe_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByLiabilityClassAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_2e187656-4365-4509-be76-4fb5b9e9446d_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_e267a44c-d2c3-4a7f-80de-7b2227e69801_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_2fc226b5-477c-4fe4-843b-d26dfce4e82e_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_us-gaap_SubsequentEventTypeAxis_770fbc6b-736c-4fa9-9136-59279e48a1b4_terseLabel_en-US" xlink:label="lab_us-gaap_SubsequentEventTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_b5918aa5-fcc1-4b36-a3c3-bf4eeebd7eea_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from the exercise of stock options for common stock</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" 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_22e069f5-3ec1-4449-aced-654c12b28b97_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightConversionStockPriceThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_ContingentConsiderationLiabilityShares_12d0b0b3-e12a-41ea-b794-96e07d0344a2_terseLabel_en-US" xlink:label="lab_tlsi_ContingentConsiderationLiabilityShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares unvested (in shares)</link:label>
    <link:label id="lab_tlsi_ContingentConsiderationLiabilityShares_label_en-US" xlink:label="lab_tlsi_ContingentConsiderationLiabilityShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Contingent Consideration, Liability, Shares</link:label>
    <link:label id="lab_tlsi_ContingentConsiderationLiabilityShares_documentation_en-US" xlink:label="lab_tlsi_ContingentConsiderationLiabilityShares" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Shares Unvested</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ContingentConsiderationLiabilityShares" xlink:href="tlsi-20240331.xsd#tlsi_ContingentConsiderationLiabilityShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ContingentConsiderationLiabilityShares" xlink:to="lab_tlsi_ContingentConsiderationLiabilityShares" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_2647777f-db9e-4e29-9a68-42640813fa2a_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember_e7dfc3a1-3072-4f21-b1f9-f99adfd69af0_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsSeriesB3WarrantLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series&#160;B-3 warrant liabilities</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" 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" 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-20240331.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_ConvertibleNotesAndWarrantsMember_3fff9ef3-fab3-4cd1-84fb-a60a344be737_terseLabel_en-US" xlink:label="lab_tlsi_ConvertibleNotesAndWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Convertible Notes and Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ConvertibleNotesAndWarrantsMember" xlink:href="tlsi-20240331.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_fa77428a-11a8-4ddf-93fd-2e7b2f07a1b8_terseLabel_en-US" xlink:label="lab_us-gaap_SharePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_19b6d477-096f-4bd3-8c4f-3963e543fc86_terseLabel_en-US" xlink:label="lab_tlsi_A2009PlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">2009 Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_A2009PlanMember" xlink:href="tlsi-20240331.xsd#tlsi_A2009PlanMember"/>
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    <link:label id="lab_tlsi_DerivativeInstrumentPeriodAxis_7e210f56-4a18-4da3-8007-9a7b13bafde6_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Derivative Instrument, Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodAxis" xlink:href="tlsi-20240331.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_a301866d-d919-4765-8daa-33bab65015cd_terseLabel_en-US" xlink:label="lab_us-gaap_TemporaryEquityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_dei_EntityRegistrantName_d1a85dec-866b-4ebe-98d7-beee4827550f_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_d529b409-7748-4e14-9958-2f46346f4dc0_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_GainLossOnEquityIssuance_2a0ab2b2-1312-47f3-99f4-be7fb28d194e_terseLabel_en-US" xlink:label="lab_tlsi_GainLossOnEquityIssuance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss on equity issuance</link:label>
    <link:label id="lab_tlsi_GainLossOnEquityIssuance_155d0e4b-e1a5-4d8c-bdd7-e66edfb9004f_negatedTerseLabel_en-US" xlink:label="lab_tlsi_GainLossOnEquityIssuance" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Gain (Loss) on Equity Issuance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_GainLossOnEquityIssuance" xlink:href="tlsi-20240331.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_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_f633bedf-f3e6-473e-9662-e9e53418da48_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of contingent earnout liability</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_9715e5e7-802c-4a37-8b3c-0dc592a0e7a4_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of contingent earnout liability</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration Arrangements, Change in Amount of Contingent Consideration, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:to="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationLiability1" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PublicWarrantsMember_795a641e-21bd-40d8-8f59-d357ea9dd866_terseLabel_en-US" xlink:label="lab_tlsi_PublicWarrantsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Public Warrants</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PublicWarrantsMember" xlink:href="tlsi-20240331.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_c3a7f019-68a9-4599-a130-3a8f9b150fd5_terseLabel_en-US" xlink:label="lab_dei_DocumentPeriodEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_13bc355c-777f-4f27-8b0c-4152de3db64a_terseLabel_en-US" xlink:label="lab_tlsi_SaleOfStockAuthorizedAmountValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_e8d64a94-9f76-4dbf-9a60-191fdc042eb3_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendRatePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_46d8424d-4c52-4e62-8038-c69360970a31_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Convertible 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" 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_dei_EntityCentralIndexKey_8bfbfbac-95ca-4f71-aa97-94b05b52f620_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_7d91e860-43b6-42cb-a2e4-4368574d112c_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfWarrantOrRightAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_87aacad4-fea4-4b9d-b373-f810d9bf470c_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of SEPA and warrant liabilities</link:label>
    <link:label id="lab_us-gaap_DerivativeGainLossOnDerivativeNet_da98b388-b556-4c81-a785-ae33402490d7_negatedLabel_en-US" xlink:label="lab_us-gaap_DerivativeGainLossOnDerivativeNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Change in fair value of warrant and SEPA liabilities</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" 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_4df3e5c0-6a3c-444e-8772-f1777eb9d676_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnSaleOfPropertyPlantEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" 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" 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_IncomeTaxExpenseBenefit_3041f76d-e393-4473-88ee-4c08ce847e3d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax (expense) benefit</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" 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_f6fb5a74-2457-4d49-b0af-ee4b4db66e77_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryFinishedGoodsNetOfReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_tlsi_ClassOfWarrantOrRightTerm_9d40bacb-eba0-46c3-93c5-3af9f550066a_terseLabel_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Warrant expiration period</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightTerm_label_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Term</link:label>
    <link:label id="lab_tlsi_ClassOfWarrantOrRightTerm_documentation_en-US" xlink:label="lab_tlsi_ClassOfWarrantOrRightTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Class Of Warrant Or Right, Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ClassOfWarrantOrRightTerm" xlink:href="tlsi-20240331.xsd#tlsi_ClassOfWarrantOrRightTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ClassOfWarrantOrRightTerm" xlink:to="lab_tlsi_ClassOfWarrantOrRightTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ReverseRecapitalizationTransactionCostsPaid_f57bb352-8ed7-41d0-8a70-3f5ceaf1dd11_terseLabel_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationTransactionCostsPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Reverse Recapitalization, Transaction Costs Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationTransactionCostsPaid" xlink:href="tlsi-20240331.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_51f40474-19db-4e54-bcc5-9a29ac6d5317_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_b8299637-e291-489b-8020-93726ea35cd9_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockWarrantMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Preferred Stock Warrant</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PreferredStockWarrantMember" xlink:href="tlsi-20240331.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_LoanFacilityMember_01b03861-988f-460c-bfdd-32d5da5e0a03_terseLabel_en-US" xlink:label="lab_tlsi_LoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Facility</link:label>
    <link:label id="lab_tlsi_LoanFacilityMember_label_en-US" xlink:label="lab_tlsi_LoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Facility [Member]</link:label>
    <link:label id="lab_tlsi_LoanFacilityMember_documentation_en-US" xlink:label="lab_tlsi_LoanFacilityMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Facility</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LoanFacilityMember" xlink:href="tlsi-20240331.xsd#tlsi_LoanFacilityMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_LoanFacilityMember" xlink:to="lab_tlsi_LoanFacilityMember" 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" 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_d480b16b-b3b6-43b2-876d-b2db3aef73b5_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Derivative Instrument, Period One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodOneMember" xlink:href="tlsi-20240331.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_ff760c19-d3bb-40ff-b2d3-048f27b81a05_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale of common stock</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues_c99c46c9-3a65-4d64-83ae-6d69fa3da282_verboseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueNewIssues" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" 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" 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_f29f06c9-8c98-41ec-aa17-0b9511319bb5_terseLabel_en-US" xlink:label="lab_us-gaap_EquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stockholders&#8217; 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" 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_d6d6ae07-8494-48e4-9196-95a9fea7fd16_terseLabel_en-US" xlink:label="lab_us-gaap_InventoryDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_74e1a7ed-2903-4830-81c2-4ea3c847b112_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromContractWithCustomerExcludingAssessedTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_us-gaap_PreferredStockDividendsIncomeStatementImpact_78aadee7-cd5f-4977-8734-8e82ea4b29db_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockDividendsIncomeStatementImpact" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Undeclared dividends on Series A preferred stock</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" 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_LongtermDebtTypeAxis_ac49ef4f-d5b7-4224-bd7e-e240accccea4_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AmendmentFlag_2b21a73c-6f68-4092-b7f2-51fbd1ba8e1f_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_60871d47-71e3-4396-b4d1-9105572959e8_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodStockPriceTrigger" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_IntangibleAssetsDisclosureTextBlock_ad9a7f62-bc8c-4bec-a8d7-5701c9b0de7d_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Assets</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_IntangibleAssetsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:to="lab_us-gaap_IntangibleAssetsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice_6b187519-6614-417a-b1c1-d70a2f8d5b6b_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockNumberOfTradingDaysVolumeWeightedAveragePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_A2023PlanMember_ca047fd3-5528-4121-ac7d-80f76b9d1098_terseLabel_en-US" xlink:label="lab_tlsi_A2023PlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">2023 Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_A2023PlanMember" xlink:href="tlsi-20240331.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_CommercialMilestoneMember_6a7ce6b8-568b-4fb2-b123-1ac57786c555_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestoneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Commercial Milestone</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestoneMember" xlink:href="tlsi-20240331.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_83e2d587-9a8d-4102-bdf5-3944bcf4d2ea_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_a13e38a0-c492-45c3-b950-dd264cfe8fe5_terseLabel_en-US" xlink:label="lab_tlsi_PreferredStockConversionPriceAutomaticResetDurationFirstReset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_PurchaseAgreementOwnershipLimitation_7d021d13-4cb6-499c-bb07-78364993e9bc_terseLabel_en-US" xlink:label="lab_tlsi_PurchaseAgreementOwnershipLimitation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Purchase Agreement, Ownership Limitation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_PurchaseAgreementOwnershipLimitation" xlink:href="tlsi-20240331.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_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays_e397685e-9960-476d-a2b0-88676e03949d_terseLabel_en-US" xlink:label="lab_tlsi_CommonStockSharePriceAverageDailyVolumeNumberOfTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_00e659d8-62cc-4279-b3af-64b870c3a7c4_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_tlsi_ReverseRecapitalizationAbstract_label_en-US" xlink:label="lab_tlsi_ReverseRecapitalizationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" 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" xml:lang="en-US">Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ReverseRecapitalizationAbstract" xlink:href="tlsi-20240331.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_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized_4384250a-3f85-41d8-a07f-de378073c9a0_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional number of shares authorized (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Additional Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfAdditionalSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpensesAbstract_a3a10527-50b6-4eb3-a3c9-d57275eb3eb1_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_1168fc70-ad89-4ea2-9435-652f7c2c2721_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquirePropertyPlantAndEquipment" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" 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" 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_03438536-24c5-41e4-8728-d03aded76290_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_39d53dec-7f54-481e-910f-c0e05b118f16_terseLabel_en-US" xlink:label="lab_tlsi_PaymentsForAssetAcquisitionMilestoneAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_fabc36ad-71f8-4a16-9ce9-97865beb62c6_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" 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" 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_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_4d387a69-f786-4321-b8de-a7b8f3a7a129_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_49efb258-e6a2-48f9-b2cf-38dc90d1599a_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Commercial Milestone Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestoneTypeDomain" xlink:href="tlsi-20240331.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_b5680667-5cfa-436c-89cf-b87d265cea0f_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Derivative Instrument, Period [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodDomain" xlink:href="tlsi-20240331.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_88398513-443a-4c57-aec5-53d5c3fbd39c_terseLabel_en-US" xlink:label="lab_tlsi_SeriesAConvertiblePreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Series A Convertible Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_SeriesAConvertiblePreferredStockMember" xlink:href="tlsi-20240331.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_6be2fb9f-93fe-4c8b-b097-58e091c6d3f6_terseLabel_en-US" xlink:label="lab_tlsi_LeaseLiabilityCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Lease Liability, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_LeaseLiabilityCurrent" xlink:href="tlsi-20240331.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_5e392f87-2ef9-481a-bb31-83196062447c_terseLabel_en-US" xlink:label="lab_tlsi_CommercialMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Commercial Milestone Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_CommercialMilestoneTypeAxis" xlink:href="tlsi-20240331.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_AssetAcquisitionConsiderationTransferred_d46f1bc6-ca71-4a12-a60a-05827bbf98ba_terseLabel_en-US" xlink:label="lab_us-gaap_AssetAcquisitionConsiderationTransferred" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_a43bee65-0597-4d07-8b3c-feeb2630239a_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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_574f9a72-ae39-41f7-91a1-9cf7942e6664_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentContingentConsiderationLiabilityEarnoutPeriodThresholdConsecutiveTradingDays" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" 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-20240331.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_806da85d-386d-4eae-9d31-86662a8abde9_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Decrease in cash, cash equivalents and restricted cash</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Including Exchange Rate Effect</link:label>
    <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_f73c1ea5-fcc2-4aa3-87cb-981e15f5a4f5_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Derivative Instrument, Period Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_DerivativeInstrumentPeriodThreeMember" xlink:href="tlsi-20240331.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_SecuredDebtMember_5703222b-6651-4e13-9097-8fd51334823d_terseLabel_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Secured Debt</link:label>
    <link:label id="lab_us-gaap_SecuredDebtMember_label_en-US" xlink:label="lab_us-gaap_SecuredDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Secured Debt [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SecuredDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SecuredDebtMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SecuredDebtMember" xlink:to="lab_us-gaap_SecuredDebtMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityComponentDomain_679f92e3-f1b9-4465-aed2-229f68476447_terseLabel_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityComponentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_EquityComponentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityComponentDomain" xlink:to="lab_us-gaap_EquityComponentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_853e4bd1-5711-4e48-991d-27499e7429a9_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock options exercise price, percentage of fair value</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Purchase Price of Common Stock, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardPurchasePriceOfCommonStockPercent" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember_64ebc1f4-3bc1-4c50-869b-50376a76a933_terseLabel_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expected probability of draws</link:label>
    <link:label id="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember_label_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Probably of Draws [Member]</link:label>
    <link:label id="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember_documentation_en-US" xlink:label="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Probably of Draws</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:href="tlsi-20240331.xsd#tlsi_MeasurementInputExpectedProbablyOfDrawsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:to="lab_tlsi_MeasurementInputExpectedProbablyOfDrawsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_ba2be030-2bd2-4eef-9c15-bc3f5dafbb80_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_b26f0678-b2ee-4d2a-953e-ede52ca822fe_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average common shares outstanding, basic (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_a1a3569b-12cb-47f6-b466-6415f82f19db_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2023/dei-2023.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_0358f510-cfbf-4867-8957-34bf4243a150_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Loss from operations</link:label>
    <link:label id="lab_us-gaap_OperatingIncomeLoss_label_en-US" xlink:label="lab_us-gaap_OperatingIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_OperatingIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingIncomeLoss" xlink:to="lab_us-gaap_OperatingIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription_8e097600-9ecc-4b64-b6c3-c4a37b681c1c_terseLabel_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reclassification</link:label>
    <link:label id="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription_label_en-US" xlink:label="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reclassification, Comparability Adjustment [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_PriorPeriodReclassificationAdjustmentDescription"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:to="lab_us-gaap_PriorPeriodReclassificationAdjustmentDescription" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned_ed431674-67c5-49f1-99e0-6a86322e5e20_terseLabel_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise of options (in shares)</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned_label_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period, Net Of Shares Returned</link:label>
    <link:label id="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned_documentation_en-US" xlink:label="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period, Net Of Shares Returned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned" xlink:href="tlsi-20240331.xsd#tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned" xlink:to="lab_tlsi_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisesInPeriodNetOfSharesReturned" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_ProceedsFromReverseRecapitalization_4e3cf6f5-e7ac-4f7c-bc96-fa82579c6bfa_verboseLabel_en-US" xlink:label="lab_tlsi_ProceedsFromReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from business combination</link:label>
    <link:label id="lab_tlsi_ProceedsFromReverseRecapitalization_label_en-US" xlink:label="lab_tlsi_ProceedsFromReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Reverse Recapitalization</link:label>
    <link:label id="lab_tlsi_ProceedsFromReverseRecapitalization_documentation_en-US" xlink:label="lab_tlsi_ProceedsFromReverseRecapitalization" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Reverse Recapitalization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_ProceedsFromReverseRecapitalization" xlink:href="tlsi-20240331.xsd#tlsi_ProceedsFromReverseRecapitalization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_ProceedsFromReverseRecapitalization" xlink:to="lab_tlsi_ProceedsFromReverseRecapitalization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_ea3b9256-dcb4-4aa8-8cdf-3bcae1dcb714_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2023/elts/us-gaap-2023.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_StandbyEquityPurchaseAgreementMember_e8d3db2d-0a9a-43fa-91bb-761c9fbf82a0_terseLabel_en-US" xlink:label="lab_tlsi_StandbyEquityPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" 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" 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" xml:lang="en-US">Standby Equity Purchase Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_StandbyEquityPurchaseAgreementMember" xlink:href="tlsi-20240331.xsd#tlsi_StandbyEquityPurchaseAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_StandbyEquityPurchaseAgreementMember" xlink:to="lab_tlsi_StandbyEquityPurchaseAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones_489a5900-2981-4627-a821-5b3632e2ffbd_terseLabel_en-US" xlink:label="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of commercial milestones</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones_label_en-US" xlink:label="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Number of Commercial Milestones</link:label>
    <link:label id="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones_documentation_en-US" xlink:label="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Acquisition, Number of Commercial Milestones</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:href="tlsi-20240331.xsd#tlsi_AssetAcquisitionNumberOfCommercialMilestones"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:to="lab_tlsi_AssetAcquisitionNumberOfCommercialMilestones" xlink:type="arc" order="1"/>
    <link:label id="lab_tlsi_DerivativeFinancialInstrumentsTrancheLiabilityMember_7d5818ae-58e6-4153-9eaf-c046558702b9_terseLabel_en-US" xlink:label="lab_tlsi_DerivativeFinancialInstrumentsTrancheLiabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Series&#160;B-2 tranche liabilities</link:label>
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