grease one's palm
grease one's palm or grease the palm {slang}
1. To pay a person for something done or given, especially dishonestly; bribe.
Some politicians will help you if you grease their palms.
2. To give a tip; pay for a special favor or extra help.
We had to grease the palm of the waiter to get a table in the crowded restaurant.
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Source: A Dictionary of American Idioms