Unfortunately there is no way to manually edit this list, so I (try to remember to) ignore it and use my browser bookmarks to manage my project access instead.
Closing to focus the discussion on this topic opened by staff: https://forum.inaturalist.org/t/ideas-for-your-recent-projects/1012 (and this bug report https://forum.inaturalist.org/t/recent-projects-list-in-header-does-not-show-recently-created-projects/3427)