We originally had a mirror that was glued to the wallpaper (actually vinyl wall covering) as a backsplash over the stove and replaced it with ceramic tile. The mirror came off without too much problem, but removing the vinyl covering was pretty difficult. Since we were installing ceramic tile attempting to adhere it to vinyl didn't seem to be a good idea so we worked it down to the wall surface (plywood). However, if you plan on covering it with a peel and stick product and the existing wall covering is solid, I would try just sticking to the existing surface first. It will probably hold up well and if it doesn't, then I would look into removing the wall covering. Good luck.
Lou
05 Travel Supreme Envoy