Thanks Wojtek, Robert, and Andy. I suggested the solution to that "oily" stain to myself in my description of it. I gave it a light wipe with white spirit and it was largely removed. This was an old piece of tape I'd had sitting on my cutting board for quite some time, so I don't know whether it had degraded or absorbed oil from the mat or somewhere else. Anyway, something I'll be careful of in the future...