Assuming you're talking about wood grip panels . . .
I have had good luck by laying the panel on a stack of soft rags with the medallion down, and then using a punch that is just smaller than the medallion stud to gently tap the medallion out into the cushioning rag pile.
To reinstall, I just barely squeeze the diameter of the stud to reduce the peened points and then gently squeeze the medallion back into place with my fingers. I do not attempt to re-peen the stud, and I haven't seen the need to use glue.
I have yet to break anything. That said, this is JMHO, YMMV, close cover before striking, objects in mirror are closer than they appear. etc. :wink:
The grip can crack across the hole when driving out the meds.
I try to carefully mitigate a bit of the peening on the end of the stud before driving out. It's usually only in two places, at the end of the punch slot; either pinching the end of the stud with needle nose pliers or a very small pointed stone in a Dremel tool.