I dont think Garmin will do anything for you. I believe that the 2610 is listed as obsolete and no repair is available. My 2730 did the same thing and the digitizer needs to be replaced. I have been unable to find a digitizer.
I soaked mine in hot water and took the rest off with a soft Popsicle stick about 3 years ago. If you get the sticky stuff off, it looks pretty much like new under the layer that is coming off. I am still using mine in the car 3 years later with no ill effect.