The root is in a Korean-war era USAF song, "Save a fighter pilot's Ass".
That song is an adaptation of some American traditional song that goes "place a nickel in the drum, save another drunken bum", referring to putting money in a Salvation Army donation can.
So, the "grass" word was just changed to rhyme with "ass" in the fighter pilots' adaptation. Other than that, there's no special significance.
At some pilot, pilots started taking the song lyrics literally.