Yeah I kept "stripping" the t nuts. The teeth would come off then it would just spin and jam in there making it impossible to remove not only the nut, but the bolt and hold. Very nasty issue.
My experience below if anyone runs into it:
This happened for me because I made the holes too small and decided I would pull the bolts into the wood from the other side. Which worked like 80% of the time. But if the teeth don't sink fast enough they bend, snap, then jam. So make big enough holes and ensure you hammer them in.
In the following order to not damage it.
1.) If your tnut heads aren't perfectly circular (most aren't because of the teeth) you can try drilling a screw through the board near the nut to lock in place then remove it. I have bent a number of screws doing this though.
2.) Try the wedge trick mentioned above, pushing the nut against the wood very firmly to prevent spinning.
3.) Try some pliers or other clamps, I would try this after the above two as you might damage/get it stuck even more.
4.) Get the angle grinder out. I have never been able to save the bolt. Maybe I need a better blade but the some of the nut melts onto the bolt making a stopper. I cut a square around the bolt, real close to it, bend it with pliers a bit, hammer it out. Then I clamp the hold to a bench and use the angle grinder to cut off the bolt so it will come out of the hold without hammering it through. Not something I would ever hope to do behind an already in place wall.
Long story short I just use the t nuts with 3 holes in them and screws instead of the teethed ones now.