I think it's a new thing Etsy recently rolled out to all shops, it's not an 'opt in' feature that you can choose or avoid. I've gotten a few orders that were 'marked as gift'. I just don't include the printed receipt, and usually reach out to the purchaser to see if they'd like a note included.
There's another place where shop owners can opt in to have a button where the customer can select gift wrapping, that option would be for an additional fee. If you didn't enable that feature you shouldn't have to use gift wrap, but I'm imagining this is even less clear to the customers!