Basically Moon Phase has only that one option to turn it on, in that menu. To "turn it off", with it already on your desktop then "right click" on the Moon Display and click on "discard panel" and it will ask you if you wish to remove it form the VWS Desktop. Click "yes"
If you are talking about the "Moon Phase" in the broadcast.jpg, then you are out of luck, and can not be removed. Because of this, I recommend that you enter your time, Lat/Long, and altitude into VWS as accurately as possible. That way the moon phase, moonset, and sunset times are accurate for your area. It is better to show the info accurately even if you don't want it there VERSUS
showing inaccurate data that you can't remove anyways.
I hope all this makes sense and welcome aboard.