You can uninstall Backbone Issue Sync from your instance by going to the manage app section. When you uninstall Backbone from your instance, the following will happen:
The sync info panel on the issues synced will be removed
Updates between the previously synced issues will no longer be synced
The issues synced will not be deleted (Backbone never deletes any issues)
If you reinstall the app within 180 days, then all your synchronization still exists and you can start the synchronization where you left off.