Solution found!
Select a cell in your query output. Depending on the format of your query, you may find you need to use a different syntax than that below.
Go to VBA and go to the immediates window.
Type:
set qry = selection.listobject.querytable
qry.parameters.delete
Note - this will delete all your parameters and you will then have to go re-set the ones you want. The next time you refresh, Excel will prompt you for the settings.
I would have thought you could, for example, do qry.parameters(5).delete, but I could not find a way to make that work
it is also helpful to use qry.parameters(1).name = "StartDate" or whatever you want, altho if you re-order or restructure your query, "StartDate" is always going to be the first Parameter, even if you use it for a different purpose, until you rename it.