Thanks for reaching out.
I think that's a great idea to allow your customers to personalize their gift cards! Could you let us know which theme you are using? You may be using a theme that allows your customers to add a note to their order within the Cart page. If you navigate to the Theme Editor, you can then choose to edit the cart page and enable cart notes. I took a screenshot from my test store to show you the sections I am referring to:
We have a great step-by-step to enable order notes on your cart page to help walk you through the process.
Looking forward to your reply, happy to help out!