Form collection when product is added to cart

We sell gift boxes that include a personalized card. I want to collect a simple form from the customer when they add a gift box to their cart. Ideally a popup or form for them to fill out with the message to the gift recipient. I want this data to stay linked to their order, not sent to me by email, and viewable when our fulfillment team prints out their order. Here is how it works on our existing website through squarespace: https://www.fablesoapco.com/shop/knmtl7uvvbbm9vy8mm93glizv0iaj4