Try a Mr. Clean Magic Eraser. Either the name brand or store brands are fine (like Walmart's), just as long as it's the "original" variety with no soaps or additives. Before use for the first time, wet and squeeze it repeatedly just to be sure. If it foams or has a strong fragrance, you have the wrong kind.
To clean the splash guard, wet it, squeeze out all the water you can, and wipe. The grunge will come right off. No special precautions necessary, it's aquarium safe, and also excels at cleaning algae from the inside of acrylic tanks.