One common synonym for the phrase "oiled someone's palm" is "bribed." This often implies that someone has used money or gifts in order to persuade someone else to do something that they wouldn't otherwise do. Another alternative phrase is "greased someone's palm," meaning the same concept of using payment or gifts to influence a decision. A more subtle alternative may be "sweetened the deal," suggesting that someone has provided extra incentives or benefits to make an agreement more appealing to the other party. Regardless of the phrase used, the implication is always that someone has used unethical means to achieve a goal or advantage.
