To keep back rightfully (a part), as if by cutting off, so as to diminish a sum due; to take off (a part) from damages; to deduct; as, where a landlord recouped the rent of premises from damages awarded to the plaintiff for eviction.  [1913 Webster]

 To get an equivalent or compensation for; as, to recoup money lost at the gaming table; to recoup one's losses in the share market.  [1913 Webster]

 To reimburse; to indemnify; -- often used reflexively and in the passive.  [1913 Webster]