I don’t think there’s a setting for this. The lowest effort option would probably be to display: none the icon in CSS & delete each auto-inserted note that the thread has been unlisted.
edit: This wouldn’t be impossible to discover by looking at the page source in the browser, but as it is immediately noticeable when the poster posts in their thread & it doesn’t appear at the top of Latest, I’m assuming we’re not trying to be massively sneaky here. They’ll almost certainly know.