Personally, the ITG led by Gambit would be the ultimate "gray area" type of organization. I don't think Gambit would allow many of the activities that would undoubtedly be happening prior to his arrival. With that, before and after he's the head, I can see certain characters, yes even hero-types, using arms of the organization for a means to an end.
Misty Knight- Misty is definitely something of an information broker. She has to have multiple sources to function as a private-eye. Of course I don't think she'd have anything to do with the Guild's more illicit activities but they'd would more than likely have information and connections that she could exploit. Especially after she realizes any changes to the organization that would make them more palatable.
Maria Hill/SHIELD- SHIELD, like Misty, operates based on information. Having a world-wide black-market network being headed up by a hero-type like Gambit would be a great asset to the organization, even more so because Gambit probably owes them a chip or two by popping in and off their radar. I'd love to see Maria and/or Mockingbird and Gambit to have some sort of ongoing working relationship. Favor for a favor type of deal. I could see them telling Gambit; Here's the deal... clean up your house, and we'll try not to haul you in every times something goes missing in the world.