A sharp knife and some diligent handwork will remove the embroidered aircraft.
Unless it's been in service for a while and/or been washed a few times, this will probably not leave any trace of what's ever been there.
Oh, and stay away from pilot shops from now on. Buy stuff online, but do it in two stages. Make your shopping list on day one, store it, and on day three review the shopping list to see if there's only stuff on there you really need. Take off whatever you don't really need, and do not add anything else back onto it. Then order.