Answer:
It would be "To offset processing fees charged by credit card companies".
Step-by-step explanation:
It wouldn't make sense to protect credit card users from ID theft, since that is taken care of at the credit card company's level.
This specific discount wouldn't necessarily bring in more customers since half the demographic is probably either cash or credit card anyway.
Lastly, credit card companies due charge fees for the use of credits cards, so a company would use this tactic out of fairness for it's customers and the profit of the business.