I removed the labels from 200 well worn Majestic Star snappers. Took a while and not my idea of a good time, but it can be done. Sorry, only have an after pic.
What I did was take an Xacto knife at a shallow angle starting at the outside of the inlay and cut through the clear plastic layer. Make about 1/4 inch long cut towards the center. Takes a little effort, so be careful! The idea is to get a one side of the cut part to stick up a bit.
From there you take a small pliers and grab onto the plastic. Take your time and keep re-gripping near the chip as it comes off, otherwise it may tear. With a little practice, you can peel the entire cover off in one piece.
Once that is done, the vinyl part remains. With an eyedropper apply a few drops of non acetone nail polish remover. The inlay will magically soften and come off with tweezers. It gets easier with practice!