When a man is possessive of a woman (boyfriend/husband/etc), he doesn't allow her to talk to other men, hang out with her friends or anything that might threaten his control over her. There can be varying degrees of possessiveness. In this case, Walter is saying he's not possessive at all (not in the least possessive) so he doesn't get worried when she talks to other men. At least that's what I'm guessing based on the context.
To break down how that sounds, it's trying to say it's even less than the smallest amount possible. So even if he was a tiny bit possessive, he's even less possessive than that.