It irritates the sh*t out of me too. I really wish there was some way to turn off receiving notifications from the Amazon app market the same way you can for virtually every android app you install including the android market.
Maybe I'm wrong but I don't think it was always like this and it only started happening with the latest update. Right now, I contend myself with going to the settings and force closing it the app. That seems to work.
Who knows? If I get irritated enough with it, I might just go ahead and uninstall the sucker.