In this case we just need to cause an error of any type where the pipeline doesn't execute and then in the UI it no longer shows an option to refresh a specific table, leaving only a full refresh as an option. In this case we removed the specification of which instance type the pipeline uses and this causes a quota error and yields the situation that I was describing.
Here is a screenshot that shows when the pipeline fails that the UI no longer offers a way to select which table to refresh.