He wouldn't. Tony Stark was physically incapable of abandoning something once he put his mind to it. This may not have been the one she'd known at home but he was still the man he was. There was no way he could walk away from something important to him. What this was, very simply, was Tony not getting over the fact he was worried about her. That maybe just maybe, the great Tony Stark was starting to care. Felicia was happy enough to let him flounder around in the mistaken opinion that it bothered her what he thought.
It didn't of course. Not one bit.
But when she got off the roof Tony actually seemed to relax. Yup, he didn't care at all. That said she'd scare him more when she got him to New York. All the museums, all the beautiful art New York had to offer. There was an analogy about kids and candy stores. And she'd be there with an oh so heroic hero type. So clearly she couldn't do anything nefarious. Clearly she'd be on her very best behavior. Even if he had insulted her, "...pockets?" she said coolly raising an eyebrow at the very thought of it. "Pockets? Seriously? Oh come on, I am so far above pickpocketing its not even a thing. But you don't need to beg me to do anything. I would never impugn upon your heroism Tony, and I'm fairly sure even I wouldn't stand a chance against that suit of yours if I did decide to find something pretty for my apartment."
And that would be her cover story. Then she'd claim womanly reasons for running off for a bit, go steal something pretty and he'd be none the wiser. Hero status maintained, and Felicia did her job. Everyone happy and they got New York out of it. Shows, fabulous meals and in general everything either of them could want, if only for a few days.
"Oh someone could could they?" He really did like to think he had an answer for everything, didn't he? Always with that wit. She'd have to do something about that. "Don't you know I always land on my feet?" she teased, returning the smirk in kind. "I mean not that I don't like seeing the heroic side of you on occasion but you won't need to rescue me Iron Man. Even if you would enjoy it."