Thanks for posting in the Community, Julie84.

We can only import invoices via Square, transactions will be downloaded automatically as invoices and payments. Other than these transactions, we don't support them yet. I would like to attach this article: Sync Square with QuickBooks Online. It contains information that helps us to know more about it.

Please know that I am always here to assist and guide you in case you need one. I hope you're having a great day. Take care!