When you save a group content menu link, it redirects you to a different form for the same menu link. If you have sufficient permissions the form looks largely the same as the one you were just on, but for most users they will just get access denied.
This modules uses the form class for menu link content items. That mostly works, except (and this is true also for the delete link), the submit handlers for the form class setup a redirect (without honoring any redirect URL set in a query destination parameter) back to the canonical URL. The module will need to build its own form classes for edit and delete of menu items.
Fixed
1.0
Code