Disclaimer: This is all just spitballing and curiousity, do not get too ic outside the fact that the Templars use gems to control the mages.
However, I was curious, outside of dying, I wonder if theoretically you could ever get rid of a gem...
Editing out some stuff that can be found out IC.
Try throwing your self in a volcano?
Better yet never get a gem and remain one of those uncontrollable elementalist.
This is just one of those things that is impossible to discuss without delving into IC stuff. If your PC wants to remove their gem, why not try removing it and going from there.