Clint hesitates for a long moment, judging the truth of what she's saying - and then takes a breath. "What if I could help you out with that?"

He's still holding onto the character, but it's the opening he was hoping for, that he doesn't have to draw the gun.

It's also probably a bad plan, and he's glad he's not wearing an earpiece at the moment considering Coulson would likely be - probably is - yelling at him from the van, but.