Is that from inserting it (if so slow down and take time, FYI the ring does go on the bottom of the pipe on the inside to make the pipe round) or the damper resting on it? If the damper I put the rods right up against the stove pipe, I have a bit of dimple on each side from it but nothing like that.
I have taken a propane hand held torch, and got the metal red and was able to get 50% of the warping out of mine. It will never be as new, but you can easily get the majority of the ugly out. Just don't get over hot.
Place foil body damaged area on a plate of steel. Heat until red, Pound bad areas with a hammer- worked for me.
Again it doesn't get them all out, but probably close to 1/2 the bad, or really bad areas will come out.