That happened at our store today too 😭 we had over 30 drinks in cafe (all delivery or mobile) and I had to pull all the stickers to get to the drive drinks. It was a nightmare.

Crap what location was this?

It’s not against policy. You have sanitizer wipes and sanitizer gel, right? Do you use those on card readers after customer touches them? Do the same thing with registers.
Are you wearing gloves in DT? Maybe you should if you are not? Or if it happens again and you don’t want to wear gloves, just use a sanitizer wipe to hold their phone or card.

If I were you, I wouldn’t even take their phone (per company policy) and just ask them if they want to use their card instead. If they want stars, they can call customer service and tell them what happened and they will add stars to their account.