Customers will need a data connection to save their digital stamp cards to Apple Wallet or Android Pay.
Customers will need to have a data connection in order to see the current number of stamps collected, rewards available, and any updates that you send to them.
Note: you can still issue stamps and redeem rewards on a customers' card if they don't have a data connection. Their stamp card simply will not update to show their latest number of stamps & rewards. However, their stamp card will update as soon as they are connected to data.