Brachos 8:3

Bais Shammai says that, after washing hands for the meal, one dries them with a towel and places it on the table. Bais Hillel says to place it on one’s seat. (The difference of opinion is based on concerns regarding spreading ritual impurity.)

Brachos 8:4

Bais Shammai says that the crumbs of the meal are swept up before washing mayim achronim (hand-washing after the meal). Bais Hillel says that the diners wash mayim achronim before sweeping up the crumbs.