When a customer is choosing to add a gift wrap, the gift wrap product is being added to their cart, increasing their total amount of the order (if you chose that the gift wrap price is more than 0).
After the gift wrap product is being added to the cart, the cart refreshes in order to show the customer the added gift wrap product and the new total price:
That gift wrap product is an actual product in your store, exactly like others, so in order to change details about it - like its name, description or image you can simply edit it from the your store's admin dashboard products section (https://your-store.myshopify.com/admin/products).
Open your store's admin dashboard (https://your-store.myshopify.com/admin) and click on Products in the left sidebar:
Then, find the gift wrap product, and click on it. Its' details screen will come up:
From here you can change all of the gift wrap product's details like its name, image and description.
Please note that it is recommended to change it's price from the Super Gift Options App Dashboard.