Those emails are an entirely unrelated notification about critical security updates.
Amazon is updating their website and needs to make sure all your old Kindles support 21st century crypto.
Mostly warning people that they need to finally update their devices, although the K1 got a patch for the cacerts file.
If your K4NT was on fw4.1.3 then it is fine. IIRC that security update appeared around August of last year.