What is the best alternative to Stamp Me on iPhone?

mobile-pocket loyalty cards, S tier, #1 in loyalty card wallet.

Is there a free alternative to Stamp Me?

Yes: mobile-pocket loyalty cards (S tier, #1) is free, with no in-app purchases.

Yes. 2 apps rank above it in loyalty card wallet: mobile-pocket loyalty cards (#1), WinStamp - Loyalty Card (#2).

Stamp Me is S tier, #3 of 7 in loyalty card wallet. Here is everything that competes with it on iPhone, in tier order.

1
mobile-pocket loyalty cardsS
Free · ★ 4.7 · 11,193 ratings · score 95
Stores loyalty and membership cards in one app, with barcode and QR-code support that works offline.
2
WinStamp - Loyalty CardS
Free · ★ 4.9 · 4,020 ratings · score 93
Stores loyalty card stamps from participating businesses in one app, using a personal QR code shown at checkout.
4
Card Manager: Digital WalletA
Free + IAP · ★ 4.7 · 2,016 ratings · score 87
Stores gift, loyalty, membership and other cards in one app, with Apple Wallet support and offline use.
5
Pass2U Wallet - Add store cardA
Free download · ★ 4.2 · 2,894 ratings · score 86
Stores store cards, coupons, event tickets and boarding passes as digital passes in Apple Wallet, created by scanning.
6
Key Ring Rewards Card WalletB
Free · ★ 4.6 · 20,107 ratings · score 79
Stores loyalty, membership, and library cards digitally and lets you build and share shopping lists.
7
BJs Wholesale ClubB
Free · ★ 4.8 · 1,077,579 ratings · score 74
BJ's Wholesale Club app for members: coupons, gas prices, club details, pickup, delivery and membership access.

What is the best alternative to Stamp Me on iPhone?: mobile-pocket loyalty cards, S tier, #1 in loyalty card wallet.
Is there a free alternative to Stamp Me?: Yes: mobile-pocket loyalty cards (S tier, #1) is free, with no in-app purchases.
Does anything rank above Stamp Me?: Yes. 2 apps rank above it in loyalty card wallet: mobile-pocket loyalty cards (#1), WinStamp - Loyalty Card (#2).