Clint takes half a step back when she gets in his face, honestly a little intimidated by the sudden ferocity of her approach. He's ready to just raise his hands and try to charm her into being less in-his-face, even if she's full of shit, but then she brings up... that.

And he gets angry.

"Well, at least I was never in a compulsive lying phase like you, lady," he all-but-shouts back, getting in her face right back. "The Avengers haven't even existed for five years, let alone employed some knock-off hack like you!"