That’s actually slightly separate to the topic being made a banner.
If that’s the correct About topic that’s been made a banner then you can open its topic wrench, select Unpin, and choose the Remove Banner Topic at the bottom of the menu. That will remove it from the top of the homepage (as in your first screenshot in the OP).
For the pinned/unpinned for anon versus admin, that topic is a pinned one as it has a little drawing pin icon next to it - however, individuals can pin/unpin it for themselves, or it can be automatically unpinned if you’ve already read it [1]. So for anon it will appear as pinned, where for you it will be unpinned.
Does that make sense?
depending on a couple of settings ↩︎