Oh, I'm sure if the author had not decided to change the book cover, the next letter wouldn't have been so nice.
That said... that's (IMHO) the proper way to handle the situation, at least at first. Simply inform them that there's a problem & why. No need to start over legal threats, give them a chance to apologize, back down, and all save face.
And who else would offer to pay for the re-design?