Gift Box automatically tags orders that receive the gift with a 'giftbox' tag, which you can see in the Orders page of the Shopify admin. This tag can be used to filter and sort orders with Gift with Purchase (GWP) from the ones that do not have.
In the product information section of the order, you will note if a product was added as a gift because it will have a $0 price, which means they were added as gifts to your customers.