Tex. Tax Code § 11.439

(a) The chief appraiser shall accept and approve or deny an application for an exemption under Section 11.131 or 11.132 for the residence homestead of a disabled veteran but not the surviving spouse of the disabled veteran or Section 11.22 after the filing deadline provided by Section 11.43 if the application is filed not later than five years after the delinquency date for the taxes on the property.

(b) If a late application is approved after approval of the appraisal records for the year for which the exemption is granted, the chief appraiser shall notify the collector for each taxing unit in which the property was taxable in that year not later than the 30th day after the date the late application is approved. The collector shall correct the taxing unit's tax roll to reflect the amount of tax imposed on the property after applying the exemption and shall deduct from the person's tax bill the amount of tax imposed on the exempted portion of the property for that year. If the tax and any related penalties and interest have been paid, the collector shall pay to the person who was the owner of the property on the date the tax was paid a refund of the tax imposed on the exempted portion of the property and the corresponding portion of any related penalties and interest paid.