I think you are correct. I removed the diode but it tests good as unidirectional with a .6V drop. It does appear that the circuit has this diode directly across the 9V winding of the transformer. If this is a bidirectional TVS diode, and I think it is, it may be possible that one of the internal diodes shorted. That would explain why it tests good as a unidirectional diode.
If I operate the meter without this diode just for testing, do you think this will do any damage?