For those who do have the new option - you go to the Manage My Kindle page and find the book in question. Then click on the plus sign next to the book title, so that the cover and the order details are show. At the bottom, right section of the listing, you should see a new button: Delete This Title. One of the users on the Amazon forums has posted a picture of how it looks, which you can see HERE. Clicking on the button allows you to delete the book from your listing forever, after you confirm the delete (which warns you that you'll have to re-purchase the book if you want it back). Here's the official help info from the Amazon web site:
To permanently remove an item in the list from your account and Archived Items:
- Locate the item you wish to delete in the "Your Orders" section. If you have a lot of content, you may need to use the Previous and Next links at the bottom to navigate through all of your content.
- Click on "Delete this title" button next to the title to permanently remove the title item from your account and Archived Items.
Note that after the title is removed from your account, you will no longer have access to re-download this title unless you re-purchase it. Existing copies of this title already on your device must be manually removed. For more information on removing content from your device please see Removing Kindle Content.
One reason I can see for the new option - it lets you painlessly remove any of the free classics you have bought, as some have atrocious formatting. Also, if you have an inexpensive book that you want to buy a new version of (such as the one shown in that screenshot, above), you can now do so yourself (it's not a free upgrade, but you might not mind on a book that only costs a dollar or two and is upgraded substantially).