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Which app are you using for the books?
Ok great, to remove any book from the Kindle app(remove it from being downloaded on your device, and from being on the home screen of the app), just press and hold your finger on the book until a menu pops up, you can then choose to remove it.
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The only way to remove an item from the Archive, is to log into amazon.com and remove it from your account. You cannot remove something from the Archive as its simply a list of the books you have attached to your account, so you need to actually remove them from the account to remove them from the archive.