Weird indeed. Like @El Patron wrote, it may be something hooked to 'actionObjectProductInCartDeleteAfter', but the only module that is there is PrestaShop Checkout. Are you using it? If not, disable or uninstall.
Is the shop live so we can see it? What is the cart module that you are using? It looks quite custom, probably instead of deleting product from the cart it deletes the product totally.
A to jest w standardowym checkoucie? Raczej mało prawdopodobne, bo moduł swój przycisk wyświetla na specjalnym dodatkowym hooku przy kurierze i tym steruje sama Presta.
I've seen it many times even on a clean installation but never had a motivation to actually examine it. Can you inspect the code in the console and see if this element has any ID or class?