[jmewdscnt]

the only concern I would have is the barcode on the box. Could they use it to trace the mistake?

That's what I was referring to by Identifiable markings.

If It's been registered with the other company and they scan the return, they'd see It's not part of their Inventory, hence It'll conclude It doesn't belong to them.

Would there be a way around this? Could I remove the barcode from the box? Or claim that the wrong shoes had been inserted in the box?