Wash the plate with warm water and grease cutting dish detergent (Dawn works well), rinse with lots of water, dry with a clean towel, and don’t touch the print surface. A clean dish rag or small nylon brush will help get into the low spots on a textured plate.
Alcohol will dissolve oils on the plate (fingerprints usually), but will re-deposit them when it evaporates. Unless you wipe the plate with lots of alcohol and multiple clean towels, you are probably just spreading the oils around. Better than no cleaning at all, but not totally effective.