The one possibility is to check the reverse servo from the outside. The servo cover can be removed and the servo piston and seals can be removed and inspected.
It may also be possible to verify that the reverse band is holding the input drum or if the band or anchor are damaged. A line pressure test and scan should reveal whether the reverse solenoid is operating, and that the valves are complying.
You'll have to determine if the vehicle is worth the diagnostic time.