Hand sanitizer works on hard, non porous surfaces because it is alcohol based. Rubbing alcohol (3% strengthisopropyl) will work but be gentle and dab instead of rubbing. Also be sure that the plate's surface is smooth and not rough and not porous so that the surface glaze isn't also removed.
I'm not sure about permanent marker and cloth - soak in oxyclean? there should be some suggestions on the internet - Good luck.