This actually happens quite a bit. We surveyed the pizzeria industry a few months ago, and 78% of pizzerias believe it negatively impacts their business. It’s called a chargeback, and they can occur for a bunch of reasons. The most common of which are considered “friendly fraud,” where they don’t remember making the order or don’t recognize the charge on their card. We have a whole guide about it, and how to reduce those kinds of chargebacks.
Basically, the only way to eliminate chargebacks is to only accept card-present credit card transactions with EMV chips. That means no paying over the phone, no pre-payments online. Delivery orders would need to be paid for upon delivery, with a mobile PIN pad or a system like SpeedLine Pay. Pick-up orders would need to be paid for in-store. Most restaurants end up making the risk versus reward decision based on how much the fraudulent transactions are costing them, compared to the convenience of online and phone payments.