From an e-mail:
I’m sorry to know that you are unable to delete a expired a library loan book from your kindle for iPad.I think the customer support executives are drinking too much coffee. Or maybe not enough?
To resolve this issue by the earliest, I’d request you to please reach us by chat or phone as these types of error requires real time troubleshooting which is only possible on phone or chat.
Hence, I’d request you to please reach us over chat or phone as we need to gather more information to rectify the situation as it would be easier for us to resolve this issue over chat or phone as you can speak to our live customer support executives who can discuss the problem in detail and perform the real time live troubleshooting to resolve the issue to your satisfaction.
Expired library loans that refuse to go away seem to be a common problem with Kindles and the Kindle app. After reading this e-mail, I decided on a drastic DIY: I deleted the Kindle app from my iPad and Mac, reinstalled, deregistered (sic) and reregistered, and the book was gone.
And hence, the book was gone.