I bet the wood has a coating or top sheet as u put it and your not dealing directly with exposed wood. Anyhow just get an edge and peel it off. You can use a razor blade or knife to carefully get an edge, then peel it err on the side of cutting into the pad not the board. Then it will inevitably leave sticky stuff on there. You can use wd-40 and a old towel(rag etc) to safely get it off with some friction. You can reapply wd 40 until its gone. It won't screw up the top sheet like a solvent could. Then u can use mild soap and water to get the wd40 off.