Thanks for the replies! We didn't address the marks when we went back to do the panel change, but I'll try out both the ZEP and the Simple Green in future.

Magic Eraser got the marks off the last time I tried it, but it also took the surface luster off the paint; you could tell where I'd used it. (The Magic Eraser works like a charm for getting BX/box oil fingerprints off T-bar ceiling tiles, though!)