grease (one's) fist

To bribe one discreetly, as by slipping money into their hand. A: "How are we going to get a table without a reservation?" B: "Don't worry, I greased the hostess' fist—she promised us a table in no time." We'll grease the guard's fist so that he leaves the gate unlocked after everyone leaves the building tonight. I greased my brother's palm to stop him from telling Mom that I had a party while she was away.