Banking these items is a bad idea, as since its unique it will randomly appear in your bags or bank depending which is loaded first by the server. If you do find them in your bank start moving them back to your inventory.
This exploit works because the extra mugs are actually still in your bags just hidden since the server won't let you have multiple unique items at the same time. This is also why it sometimes changes slots in your bags and bank, and sometimes even when zoning.
In terms of deleting mugs, we know it can have dire consequences turning other items in your inventory into mugs. I'm not sure if its safe to delete the empty mugs either, to be safe don't delete anything!