I believe it is illegal (at least in some states) to use the card information for anything other than processing the payment. That is, I believe they cannot use it to track you and your purchase. This is one of the main reasons there are loyalty cards — to get you to explicitly consent to tracking.

edit: If they are allowed to track based on credit card, this would be a good reason to use Apple Pay, or some other payment method that generates a unique "card number" for every purchase.