Recognizing Mayaguez Veterans Act This bill requires the military department concerned, upon application by or on behalf of a veteran who was awarded the Armed Forces Expeditionary Medal for participation in the Mayaguez rescue operation of May 12-May 15, 1975, or who otherwise participated in such operation, to award that veteran the Vietnam Service Medal, notwithstanding any otherwise applicable requirements. Such award shall be made in lieu of any Armed Forces Expeditionary Medal awarded for participation in such operation.