Try deleting the Google Ad widget and see whether that deletes the faux widget as well. Then you have your answer.
If that is the problem, then just replace the Google Ad widget with a plain Text widget and add your code to that.
Dear John,
Thanks. That’s a great idea. I will not be able to try it until tomorrow but I will give it a shot.
And if all else fails add this to your CSS:
.tab-box-right {display: none;}