The phrase "to grease the hands" means to give someone money or a bribe in order to influence them or get them to do something for you. Full definition
If you are not using a coating then lightly grease your hands with oil and pat smooth.This will help keep the marshmallow cream from sticking to your fingers. (ourpaleolife.com)
Lightly grease your hands with coconut oil. (paleocrumbs.com)
When well mixed and thick in texture wash then grease your hands with some olive oil and shape into 6 sausages. (maplespice.com)