[His casual argumentativeness immediately gives way in favor out outright anger. Reckless he could maybe agree with (even if she's too dense to get the point and ignoring the fact that he hasn't done anything... today...) but killing Captain America? Absolutely fucking not.]
First of all, if I gave a damn about you liking me I'd be even more of an idiot than you take me for. And second, you don't know me, or anything about me other than I share the same name as a guy from your world. So get it through your creepy emotionless head: I am not him.
[He's a classic case of "doth protest too much" and not interested in pursuing that particular fact. And so he hangs up before she can say anything else stupid, and with a promise to himself to find out everything he can about this "other" Tony Stark.]