@Region Philbis,
This is the Japanese version of hot towel -
Not sure if you are referring to finger bowl or hot towel often times either also has lemon with it - from an excerpt from table etiquette
"If you want to clean your fingers, use your napkin or, if a dish has been messy to eat, excuse yourself to clean your hands in the restroom if no finger bowl or hot towel has been provided."
finger bowl
vs hot towel