Yes, Corian burn marks and other mishaps can be repaired. Some, if not too deep, can be fixed just by sanding the area. If you don't want to try it yourself you can contact the Corian dealer/installer in your area and they will make the repair so you never know there had been a repair made.
I had a bad burn on a countertop. When we built the house, we had gathered ideas we liked. It just so happened one of the ideas were tiles inset onto the countertop near the stove. My husband cut squares and inset decorative tiles that matched the kitchen decor on either side of my stove. It eliminated the burn spot. (08/30/2009)