A couple of things come to mind when cleaning and when not using your surface plate:
using some of those heavy duty shop paper towels (the soft Blue ones) get yourself some waterless hand cleaner (JoJo will work) and using a goodly amount, thoroughly scrub your plate using a circular motion, for a 24X36" plate, fold the towel into quarters and then change quarters for each quarter section scrubbed. You're going to be surprised ad the amount of dirt that comes out!. Once you've scrubbed it, take clean towels and again using a circular motion completely wipe dry the entire plate, changing the towel as needed. Once it's dry you'll find that the plate is completely clean and ready to use. Using your hand to wipe the plate to see if the plate is clean is an indicator that the environment that your plate is in is unacceptable and your measurements could be suspect. (what if you missed some?) Remember that your measurements will be taken somewhere above the surface plate and that Abby error now becomes problematic: If you push your part or height gage up onto some dirt that you missed, you have introduced a "wedge" error (Abby offset) that will cause significant measurement error. Suggestion: Make a box cover using some masonite and edge strips made of 3/4 X1" strips and protect the granite from abrasion by applying several 3/4" felt strips on the underside (where the Masonite sits against the granite) Now you've created an environment that will keep your surface plate reasonably clean until ready to use again.
Any, by the way, wash your hands before using your plate also.
Mike