COVID-19 Federal Employee Reinstatement Act This bill requires federal agencies to reinstate or compensate former employees who separated from the agency due to COVID-19 vaccination requirements during a certain period. Specifically, agencies must reinstate or compensate employees who voluntarily or involuntarily separated from the agency between September 9, 2021, and January 24, 2022, due to the COVID-19 vaccination requirements of Executive Order 14043. (The executive order required all federal employees to be vaccinated against COVID-19. A federal court blocked implementation of the order on January 21, 2022. An appellate court reinstated the order on April 7, 2022.) Employees may choose to be reinstated to their former position (or a comparable position) or to receive a payment that is commensurate with any lost pay during this time period. Employees who subsequently obtained a new federal position are entitled to payment that is commensurate with any difference in pay, if the new position pays less than the previous position. The bill also provides for the treatment of such payments or service with respect to taxes and retirement annuities, including allowing the months in which an employee was separated from service during this time period to count as qualifying service for purposes of retirement.