How do I remove a backup set only from the local database (not from the backup)?

That’s generally the default behavior shown on the screen, unless something is causing yours to be different.

Could you paste a screenshot? I expect checkboxes for both, but no yes/no unless that’s how a Mac shows it.

To borrow an image from a different article, this is what I expect. Are you getting “Delete remote files” without the checkbox (making it look mandatory), or not there at all (making it look uncertain as to what will happen)?