Kickback

Any money, fee, commission, credit, gift, gratuity, thing of value, or compensation of any kind which is provided, directly or indirectly, to any prime contractor, prime contractor employee, subcontractor, or subcontractor employee for the purpose of improperly obtaining or rewarding favorable treatment in connection with a prime contract or in connection with a subcontract relating to a prime contract.

Is also used in a non-contract context to generically refer to any under-the-table payment for help or influence in getting something of value.

The legality of a kickback is dependent on the specific circumstances including the location where it occurred.