To delete a book, go to
http://amazon.com/manageyourkindle. Scroll down to the bottom of the page and use the "Find by Author or Title" search box to find the book you want to delete. Expand the title by clicking on the + sign on the left. Then look on the bottom right of the expanded box, and you should see a button that says "Delete this Title." Make sure you are sure, because once you delete from here, you can never redownload again without repurchasing. This should delete the book from Archived Items.