Proving to him that she was telling the truth was only half the feat; Kate still had to prove that Captain America was right to give her the Hawkeye name and the equipment that came with it. After all, screwing up on a couple arrows did not--and should not--discredit her skill as a fighter and so far, he'd only caught a glimpse of that. But if he called her squirt one more time, he might just see how much more of a fighter she could be.
Kate took her bow and breathed easy again, splaying it across her chest while she paid close attention to his arrangement. Her excitement was limited to a small lopsided smile and a steady "Okay", but (and she would not admit this) it was difficult not to want to reach out and hug him. Whatever, she was allowed to fangirl a little bit.
Any chance of her acting on that was slim to none, and it was amazing how quickly Kate could go from one emotion to the another. Arching her brow, she shot him a warning stare, lips tightly pursed. “And just so we’re clear,” Kate stressed: “My name is Kate. Kate or Hawkeye. But not ‘squirt’. Unless you want me to play you at your own game huh, Mister Doof?” A playful gleam flickered in her eye this time.