Upon reflection, I think it is a calculated insult to the Germans.
There is a phrase in German which (forgive any mispelling) I recall as “in der nacht alle katz ein grau”, meaning “at night all cats are grey”. This expresses the same idea in English about congress with ladies that “they’re all the same with the lights out” (I know from personal experience that this is not true as once when I turned the lights out an unusually aggressive lady said “You touch me and you’re dead.”, but that is not important here.).
So, the Soviets are sending over a grey (or ‘gray’ for our American members :D) cat to remind the Germans that there aren’t any women in their lines and that this is the only pussy they’ll be seeing for a long time.
Which suggests that, as Nick pointed out, the cat is actually a committed NKVD operative.