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)
When reinstalling the app, all your previously created Backbone synchronization are still there. You can start synchronizing where you left off.