Washing up liquid also contains lanolin, which can leave white marks if not washed down properly. I’ve not cleaned a corrector plate (I did have a Meade 14 for 7 years but didn’t clean it and didn’t lose any limiting magnitude either over that time), but have washed more mirrors than you can poke a stick at, and white marks/streaks were certainly a problem if your like me and need everything to be pristine. It was probably this that sent me grey.
If in doubt, leave well alone.
Gary