Troop Return Of Overdue Payment Act or the TROOP Act This bill requires the military departments to reinstate individuals who were involuntarily separated from an Armed Force solely on the basis of refusing to receive a COVID-19 vaccination (i.e., covered individuals). Specifically, upon the request of a covered individual, the military department concerned must (1) reinstate the covered individual in the same rank and grade the individual held at the time of separation, and (2) include the period between the involuntary separation and the reinstatement in the computation of the retired or retainer pay of the covered individual. Additionally, a covered individual who requests reinstatement must be entitled to back pay for the period between the involuntary separation and reinstatement.