Is the Shop Payments gateway secure for credit card transactions?

Shop Pay does have the ability to store credit cards and use them later as part of the accelerated gateway flows. Other accelerated payment methods like Google Pay and Apple Pay do the same. It’s very likely that your customer is confused about that.

That said, it’s always best to follow these kind of reports through for safety and peace of mind so would suggest you contact the support team and give them as much details you have on the concern.