Discounts For Booking With Debit Over Credit?

Here's something that caught our eye while checking routes on Allegiant. As the screen shot below shows, the charge for paying with a credit card is slightly more than what you'd pay if using your debit card. It's only a $4 difference, but still. As far as transaction fees go, this strikes us as a tad strange. Allegiant is essentially giving travelers a discount for skipping credit in favor of debit: