Directly underneath the card you will see a button that says "update balance". You can change the balance to $0 and the gift card will be archived under the Purchase Receipts section in the app. Just like a plastic gift card, you will need to manually track the balance.
Some retailers will track the balance for you automatically. If the button says "refresh balance" then the retailer has opted to track the balance for you. (Not all retailers allow this). Simply click the refresh balance button and the balance will change automatically.
If you accidentally change the balance to zero or delete a card by accident, you can retrieve it. Go to Purchase Receipts in the main menu. Find your card. (Only the last four digits show in the receipt section). Change the balance back to what is left. It will then appear in your wallet and under the retailer again.
If you're not sure of a balance, go to the retailer website to find the balance, just as you would a plastic gift card.