The only reason i see why we can choose B is because its short. moreover "the amount" stands for money because generally we use Recoup in relation with monitory gains (although not always necessary) for eg: In an attempt to recoup his fortune, Jim did....
even if he hadn't used the term "the amount" it would have meant the same.
eg- the employer is entitled to recoup (or recoup for) damages.
PM me for any clarification on this.
