M.L.
I agree with the responses below about using Goo Be Gone. It works great. If you don't have that, try using eye makeup remover. It works just as well and it's something you may already have. I've used this many times to get price stickers off of products and sticky residue off of just about anything. There may be a little oily residue with both the eye makeup remover and the Goo Be Gone but just get a light soapy washtowel or dish sponge and gently wipe off the greasy residue. I use the Eye Makeup remover more than the GBG because I always have it on hand.
Good luck.