Reinstate Our Troops Act This bill addresses the reinstatement of members of the Armed Forces who requested an exemption from an order to receive a COVID-19 vaccination and were involuntarily separated solely on the basis of the refusal to receive such vaccination. Specifically, at the election of the separated individual, the bill requires the military department concerned to reinstate the individual, in the same rank and grade the individual held at the time of separation. An individual must elect to be reinstated within the one-year period following the enactment of this bill. Additionally, such individuals (enlisted members and officers) are not required to repay a bonus for failure to complete a period of service solely because such service was incomplete due to the exemption request and involuntary separation. The military department concerned must return a bonus repaid by an individual if the individual elects to be reinstated. If an individual does not elect reinstatement, the military department concerned must ensure the discharge of the individual is characterized as honorable. The military department concerned must also expunge from an individual's military service record any reference to adverse action related to the refusal to receive a COVID-19 vaccination.