I've never done it, but I seem to recall there being four clips holding it in. When I saw how it was being retained, I thought if I ever had to remove one, I'd take a couple of pieces of filament tape, fold them lengthwise so the adhesive wouldn't be exposed and slip them behind the mirror and just give a tug.
The filament tape would be stiff enough to be able to be guided into the desired position behind the "glass".
Mind you I haven't tried this, so be a bit cautious. I'm pretty sure it will work, though.