What term relates to payments for services a company is not legally entitled to?

The term that relates to payments for services a company is not legally entitled to is bribery. Bribery involves offering, giving, receiving, or soliciting something of value as a means to influence the actions of an official or other person in charge of a public or private function. This practice is unethical and often illegal, as it undermines trust in institutions and can lead to corruption.

In the context of business, bribery can manifest when a company makes payments in order to receive favors, influence decisions, or gain an unfair advantage that they would not otherwise be entitled to without such payment. The act of making a payment that secures a benefit inappropriately defines bribery, as it contravenes established laws and ethical standards.

Other options like extortion, grease money, and gifts do not specifically represent the idea of illegitimate payments for services. Extortion typically involves coercion and threats to obtain money or services; grease money often refers to small payments to expedite processes without necessarily being illegal, and gifts might not imply any expectation of return benefits or services. Therefore, the most accurate term in this context is bribery.