Yes and no.... We don't have an automatic integration with Squarespace, but we do have a way to get Gift Up! and Squarespace to work together.
They simply have no way for us to access the shopping cart to apply a discount or a gift card to it. It's a very closed system, so third-party developers & systems like ours cannot automatically work with their system. We wish it was different, but alas, not yet.
They do offer their own gift card solution available on the Commerce Advanced plan, but their gift cards can only be used online, in their own checkout system. They are also limited in terms of capability compared to what we offer.
How to accept Gift Up! gift cards on your Squarespace website
We also have a way that you can employ right now to accept our gift cards in your Squarespace store.