The Collaborative International Dictionary
Recoupment \Re*coup"ment\ (-ment), n. The act of recouping.
Note: Recoupment applies to equities growing out of the very
affair from which thw principal demand arises, set-off
to cross-demands which may be independent in origin.
--Abbott.
Wiktionary
n. A recovery of what had been lost.
Wikipedia
Recoupment is the practice, common in the music industry, of claiming an advance provided to an artist back from that artist rather than (or, as well as) from related sources. Many record labels practice recoupment, and most new artists have little choice but to accept it since they lack the negotiating power to obtain a better contract.
Recoupment is also a common practice within the insurance industry. It means virtually the same thing, but generally occurs when an insurance company has paid the benefits to a hospital and then takes back that money when they have determined that those benefits should not have been given.