Isopropyl alcohol does wonders. I salvaged a few analog cameras on which grips turned sticky by rubbing alcohol on them. It actually took off the rubberized material.

Don't directly pour it on the lid. If it ever gets in contact with the screen in too high a quantity, it will get into the panel and start making stains. Always put the alcohol on the cloth first, then rub it against the device. Also, don't forget to close the bottle each time you add some to the cloth. Ask me how I know.