I've always used a vinyl bank-bag to store my hitch in. I never thought to use it to remove the ball-drop to keep my hands clean!
This pouch is a must-have if you are one, like me, who removes the ball after each use.
I just chuck it into the spare tire wheel-well under the rear floor cover (Honda CR-V). It's heavy duty vinyl and will last a very long time if not abused.