Hi Rob,
Are there any available plugin, theme, or WordPress updates on your website? It is possible that that there might be some kind of bug that is causing the Edit icon to break and running the updates will ensure that you have all of the latest patches and fixes applied to your website.
The Edit icon visibility could also be affected by a plugin conflict and you can check if there is a plugin conflict by deactivating all of the non-Boldgrid plugins on your website to see if that restores the editing features.
Hopefully this helps you get your button link changed and please let us know if there is anything else that we can do to help!