A payment made to expedite or to secure the performance of a routine governmental action is called a

Grease payment

Explanation:

Well, common people would usually refer it as a bribe.

In most cases, businesses operation often can't be done because some elements of its practices is violating the law (such as it can endanger the environment or the consumers).

In such situations, one thing that the companies can do is giving money to the government officials who are in charge to investigate the case. In return, these officials can 'overlook' the violation and the operation can be continued.