Entries in the location bar drop down list with a yellow (blue on Mac) star at the right end are bookmarks.
You can remove such a bookmarked item that shows in the list if you open that url in a tab and click the yellow star in the location bar.
This will open the "Edit This Bookmark" dialog and you can click the Remove button to remove the bookmark if you want to remove such a bookmarked entry.

This can be a problem with the file places.sqlite that stores the bookmarks and the history.

• http://kb.mozillazine.org/Bookmarks_history_and_toolbar_buttons_not_working_-_Firefox

• Remove websites from the address bar suggestions
• Cannot clear Location bar history

I don't think we are talking about the same thing. This is a plain small white box on the second bar with a small triangle within the box, clicked on and held down brings up past sites that have been viewed with a header of history at the top followed by past view sites . There is a green arrow to the right of the outside of the box.No blue stars , this is a mac and there is no indication that these are bookmarks. The fire fox preferences that are supposed to delete these does not work. Thanks