I would say that remunerate means to pay money to someone for a service or good that they have provided. Repay is to pay back money that has been lent to you, or to do someone a favor in 'payment' for a favor they have done you. Compensate can mean to pay someone for damage that has been done to them or their property, or to make it good in some way. "To compensate for the extra hours we've asked you to do this week, we're giving you an extra day off at Christmas." Recompense means pretty much the same thing, but is used less often.

Compensate - is to pay someone for a service. recompense, remunerate, and repay - very similar in meaning - they mean to pay back a debt owed to someone else.