The San Diego Hall of Champions said it returned the trophy to the family on Friday and declined further comment.
The museum received the trophy from the family in March but never displayed it.
Bush relinquished his title as Heisman winner last year after an NCAA probe concluded that he and his family accepted improper benefits from would-be sports agents while Bush was still playing for USC.
The Heisman Trust, which was considering stripping Bush of the award, decided to vacate the title for that season.
The news was first reported Monday by the San Diego Union-Tribune.