This doesn't really occur any longer but it used to be a thing that did occur, though was generally rare.

Today of course we've got computers and networking up the wazoo, you can't get away from it. A typical person has half a dozen different networked computing devices in their home and will be using one or several at any given time. And these days everyone has a smartphone connected to the internet constantly as well.

Anyway, in terms of credit (and debit) card transactions these are generally always "online" these days. The point of sale device (a store register, a gas station pump, etc.) will be connected to a terminal which can read the credit card data and perform a transaction on your credit account. Typically these have two parts: authorization and capture. Authorization basically queries your credit account as to whether it has sufficient balance to cover a set transaction amount, which can then be reserved which would reduce your available credit (if applicable) and a portion or all of the reserved amount can then be captured within some window of time (a few days) where the balance is actually transferred to the merchant. Often times these happen in one step if the amount is known exactly ahead of time, sometimes they happen in separate steps if some kind of pre-purchase authorization of an expected amount is needed such as with purchasing gas where you "pay" first before you pump and perhaps before you even know how much you will owe.

However, our world has not always been quite so computerized or ubiquitously connected. When credit cards and such-like first started the transactions were much less automated and networked and were more similar to the way a bank used to process paper checks. In some circumstances the mere ownership of a credit card was itself a sign of having credit. And just like it is possible to pass a written check for an amount that you can't cover it used to be possible to do the same with a credit card. In ye olden times the typical way a credit card transaction was processed was via paper. A merchant would take down your credit card info (the number, name, etc.) on a form, itemize their charges and provide their merchant account details, then submit the form to be processed. At some point folks got the smart idea to provide raised embossed printing on the credit card itself so you could easily copy out the number et al onto a form with carbon paper by pressing against it, giving rise to the "knuckle-buster" contraptions used by many merchants in the '70s, '80s, and a little bit in the '90s to take down a customer's credit card info quickly (onto a form that had been pre-printed with the transaction info).

This, of course, left the merchants vulnerable to transactions that couldn't be completed successfully due to insufficient credit or fraudulent accounts or what-have-you. For some circumstances this was just a regular cost of doing business, just as with accepting checks. But almost all credit cards had a number you could call to speak to someone who could verify available credit and so forth. Many businesses had policies of verifying larger transactions this way.

One of the possible outcomes from calling the issuing bank in regard to a credit card transaction was that the merchant would be instructed to destroy or confiscate the card. This was perfectly legal, and still is today, as it would be spelled out explicitly in the terms of use and often times the card itself would have text mentioning that it was the property of the issuing bank. This outcome rarely happened simply because of a single declined transaction and was more typical of cards that were reported stolen or credit accounts that were flagrantly overspent with a pattern of multiple transactions made beyond the credit limit. And, of course, the merchant bank was fully aware of the negative repercussions this would have on the relationship with the customer but would presumably only take such drastic action when it was deemed warranted. Presumably the credit account in question would already be significantly over the limit or derelict on payments and the priority of the bank is to stop the bleeding.

This can still potentially happen today with a transaction terminal instructing the merchant to call a number for additional info where they are instructed to confiscate a card but that is almost unheard of these days. Today these problems are mostly handled by a combination of processing transactions online in real-time or of having non-connected credit card reading machines regularly pre-loaded with a list of "bad" credit card numbers to refuse to process.

The main element of fiction here is simply taking an event that was fairly rare and usually happened to people who were fairly unsurprised at it happening and transforming it into one that could happen for a single declined transaction and become a hugely embarrassing situation for an unsuspecting ordinary person.