Daresh

Did you delete the payment data from Stripe module's database tables?

Is it live to see? The classic theme should not behave like this as far as I remember...

Exactly! So the question is does this order got sent to Stripe and it will overwrite it all the time, or can it be removed on the store level (from some Stripe database tables). Probably some custom module would be required here, one that knows what Stripe does and is able to remove some information from it.

It's not easy because in general, payment modules may have their own tables in the database, storing additional data related to orders. So changing a payment method to another one would require knowing it precisely and what it requires. Maybe that's why there is no such functionality in PrestaShop. Even if you change the payment related columns in the database (prefix_orders table), the Stripe module that you have may keep some data related to that order. So to change the payment method in a clean way, it would be recommended to also remove everything related to that order from Stripe's tables.

It does not look like it's coming from the default theme, must be some additional script.

Does it show on every browser?

Yes, I thought it must be something else, the module is too simple to have such an impact

PS is good for this, maybe you missed something. Is the guest checkout turned on in back office?

This is strange, which PS version do you have?

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.

Deleted completely? With what X? Maybe you have some custom made functionality not implemented correctly.

Pojawianiem się przewoźnika steruje sama Presta, więc trzeba szukać gdzieś w ogólnych ustawieniach i warunkach tego kiedy dany przewoźnik się pojawia.

W sensie nie pojawia się w ogóle przewoźnik czy nie pojawia sią przycisk wyboru paczkomatu?

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.