523. Before Bentching

Brachos 7:11

(Necessary background information: people used to eat reclining on couches with a small table in front of each diner.) After everyone has finished eating, the tables are removed and the place where they ate is swept. After this, the diners wash their hands. This is done in order to avoid having olive-sized pieces of bread on the floor as one may not walk or wash over pieces of bread that size as it will ruin them. If pieces of bread smaller than olive-sized remain, it is permitted to destroy them.

Brachos 7:12

When water is brought to wash after the meal, the one who will lead bentching washes his hands first so that the person of the greatest standing will not be left sitting with dirty hands while the others wash. The rest of the diners wash one after another. We do not honor people with washing mayim achronim because honor is not extended when it comes to dirty hands, crossing bridges, or on roads, except for an entrance that is suitable for a mezuzah. Even then honor is only extended when entering.