Do I have to print restaurant loyalty cards, or is it all on the phone?

Nothing is printed. The customer's loyalty card lives on their phone, and stamps are counted against their phone number, so there is no card to lose and no stamp to forge. The card shows the live stamp count, the reward when one is waiting, and referral credits if you run referrals. Restaurant loyalty cards on paper need a stamp at the counter; here the stamp lands on its own when the order completes. You design the card on the loyalty card screen under Marketing, and every card already on a phone updates when you change the design. The Loyalty & rewards tab in the docs has a guide on designing the card.