I can’t believe that with today’s technology they can’t see that these two checks had already been deposited two months prior.
well, they can see this, which is why the items are being returned as a duplicate transaction. But this does not occur until it gets to the paying bank where the checks are written from; the bank of deposit (in this case, Wells Fargo), would have no way of knowing these were previously negotiated at another bank when they accepted them for deposit.
others have listed steps to take once the item was deposited via mobile, and many checks now have a small box on the back where you can check off it was deposited via mobile. and shredding it or tearing it in half certainly stops anyone from being able to take and deposit again.