Let’s say that you are selling an item for $10. If a customer is trying to pay for that $10 item using a reward card (card that allows card holder to accumulate mileage or hotel points) then the store owner will have to higher interchange fee which can be as high as 3.5% . So in this case the store owner is paying a fee of say $0.35 for selling that $10 item.
A smart store owner might try to tell the customer that hey if you pay using cash then you need to pay only $9.75. Except that store owners were not allowed to do that as per Visa and MasterCard agreements.
In 2010, U.S. Department of justice filed a lawsuit against Visa, MasterCard and American Express citing that restricting the store owners to not to offer lower price is anticompetitive. Visa and MasterCard settled with Department of Justice. However American Express is still fighting the case.
As part of the settlement now store owners who accept Visa and MasterCard can offer lower rate for the items if they are paid through a different means (check or cash).