FYI, I specifically mentioned Aldi because they don't have loyalty cards. I understand that might not have been clear to everyone, so I'll edit my comment to make it clear.

Ah, yeah I don't have an Aldi near me so I didn't know that. Regardless, the same approach could be applied via emailing coupons with barcodes to scan at the register. It'd just be less convenient for the customer than having it automatically applied via a loyalty card.