Many thanks! Am using Tiki 21.0.
Your advice to use Unassign on the little actions menu on the "assigned modules" list worked. It's gone. Much relief.
And some surprise. I wouldn't have known that option was in the actions menu because, as you can see in the screenshot attached here, only Edit is visible. The other options - Move up, Move down and Unassign - are not. Hovering makes them just barely visible - in the screenshot the cursor was hovered over Unassign. Some sort of CSS issue? We've done a fair bit of customising of the default Bootstrap theme but nothing to my knowledge that caused this problem elsewhere in admin or on the rest of the site.
Also, just an FYI, in Admin Modules only the main Admin menu has the red X on its title bar. Besides our own menus we have a few Tiki modules - Last Visitors, Who is Online, Top Pages - and their title bars don't have a red X visible or invisible. Hovering on them shows the Move symbol .
Again, thank you very much for the swift solution.