Mop up : v.tr. Blot (a liquid) with a sponge or a rag.
Make up for a delay: make up for it.
Sponge one up: have a drink.
Sponging someone: taking someone's money. I got mopped up.
At the casino: get mopped up.
In the world of prostitution, "to mop up" is to give satisfaction to the customer. It sponge the lorry drivers of the ring road.
See Quench.