OK, so I just figured out how to do this!
I have been using "featured items" section modules to list select items on our Square online store home page. Unbeknownst to me, I didn't realize that our entire inventory was available online through the Square store using the search feature, so online shoppers could type in glass or ceramics or books, etc, to see a selection of whatever inventory we had.
So...now I have to go into EACH item and mark it as either hidden or unavailable. Hidden hides it from the search, but you can still send a link to hidden items to customers; this is great for custom sales.
Unavailable, leaves the items in the Square inventory, but makes them not searchable through the site, which is exactly what I was trying to do. So an unavailable item will still show on my Square terminal and I can ring through physical sales in the store, but the items won't be available online until I choose.
Now I can relink my Facebook and Insta shops...once I update the 400 shop items that are currently unavailable... >_<