What is Recoup?

Legal Definition
This word is derived from the French recouper, to cut again. In law it signifies the right and the act of making a set-off, defalcation, or discount, by the defendant, to the claim of the plaintiff. 21 Wend. It. 342. In another sense it signifies to recompense. 19 Ves. 123.
-- Bouviers Law Dictionary
Legal Definition
To deduct, defalk, discount, set off or keep back; to withhold part of a demand.
-- Black's Law Dictionary
Legal Definition
To set up a recoupment in defense.
-- Ballentine's Law Dictionary