Hand Towel Ring Cap

Moved into this house about a year ago, and the caps on two of the bathroom hand towel holders were missing. These caps were important because they...
A) Keep the towel ring from spinning freely in the wall mount
B) Keep the ring from falling off entirely
C) Keep the ring from making an unholy racket when drying your hands

This is my first item on Thingiverse, and the second (non-calibration) thing I printed when I got my Thing-O-Matic.

Modeled in Autodesk Inventor (only because I am so familiar with it.) but I may throw together a parametric openscad version when I get the chance. I threw together an openscad parametric version.