There was a change in functionality starting in 10.1 M050 and 10.2 that made it so that only Administrators are able to edit the Notebook link objects, where previously anyone could. A partial description can be found in CS191736.
SPR 5044939 has been filed; when this is complete the Site admins, Context admins and the link Creator will all have editing privileges for the link.
We do not yet have an ETA on when to expect this fix.
At this time specifying a specific role, is not planned to be implemented here but this Product Idea is to help expedite that consideration.