Definitions of set-off

a claim by a debtor that the amount of the debt should be reduced because the other party owes them money

Before we pay them any money for the delivery, we can claim the amount of money they already owe us as a set-off.

a claim by a defendant in a lawsuit that the plaintiff owes the defendant money which should be subtracted from the amount of damages claimed by plaintiff

The court reduced the damages awarded Smithson by way of set-off of the full amount of her previous settlements with the plaintiff.