Profile Manager MDM - Remove Safari Shortcuts Created Directly on the IPad

A little background: I am managing IPads in an enterprise environment via the Apple Profile Manager MDM. Server OSX recently added the ability to create Safari shortcuts directly from Profile Manager via the Web Clips payload, which was not available previously. This is great, and will make installing future Safari shortcuts much simpler. However, prior to this payload's availability, we created shortcuts manually on each individual IPad. Now, I'd like to delete these shortcuts, but at some point the management settings were changed and shortcuts cannot be deleted. If I try to press the icon and wait for the shaking app icon with the "x," it never happens. I see no option to delete the shortcuts anywhere in the settings, and I see nothing configured on the server side that would prevent this, especially considering that I used to be able to do so.

If necessary, I could wipe the IPads and re-apply the configuration profile, but it just seems like there should be an easier solution to this. Thanks for any help that anyone can provide.