The rubber piece that interfaces with my thumb is slipping part way off and back on as I shift on one of them. I'm tempted to try and pull it all the way off and glue it back on, but I'm not sure if I'll damage it doing so or not. It is under warranty, but if I can fix it myself I'd rather. Has anyone else dealt with this, or do you have any suggestions?

I'd do it. Before gluing you might try cleaning both the metal and the inside of the rubber sleeve with alcohol to degrease everything thoroughly, then dry well and reassemble. If that does not hold, then don't be afraid to try the adhesive.

I'd slide that grip off and shoot a little hair spray in there. Let it set up for a couple of hours before riding.

I went ahead and pulled the thumb-grip the rest of the way off, and sure enough, it's just a slip on with glue setup. In this case the assembler did not apply "enough" glue, and it simply broke loose. I'm going to clean it off as suggested and apply some proper glue; problem solved. Thanks for the help guys.