FYI,
The first link newbreed posted was not a NATS linkcode, it was URL of where NATS redirects the traffic to.
Also, the reason why you get that "expires: at end of session" most likely means that they set $config['NATS_COOKIE_EXPIRE'] to 0, that would most likely cause it, I will have to look into this though if you need to know for sure.
The first cookie that was set is the unique tracking cookie. A unique in nats is unique for 24 hours. The 2nd one is the nats code cookie, the third one, is a good question

do not think it was set by us.