Phrase origin On the arm?

The phrase On The Arm came from the Mafia.

To show their respects to the Mafia Boss who protected their neighborhood or fear of being extorted, the store owners would not allow them to pay for items.

The store owners would take their right hand and brush it against their left arm as a way of saying, "Forget about it" No charge, Free, (Fuhgeddaboudit)