I think it’s a lot of fun to imagine what would happen if Misaki learned Li was a contractor.
She wouldn’t ask his Messier Number
She wouldn’t ask his contract or his payment information
She wouldn’t ask his alias
She may ask who he works for, but she wouldn’t pry to his face if he refused to answer
She MIGHT try to look into his employer behind his back, but that depends on the situation
She would still call him Li, would half-joke, half-seriously ask for information on jobs and his real goals, she’d let his personality and past and private information stay very private. Why?
Because that’s how she treated November 11. Granted, she learned after the fact that Jack worked for the SIS, but she didn’t push for that information. She let him tell her on his own. She let all of this information be given to her at his own pace with almost no pressure from her whatsoever.
So if Misaki learned that Li was a contractor, while I think she would certainly feel betrayed for a time and view him in a somewhat different light, I think she would view him ultimately the same as she views Jack. (Or the same as Marinette views Chat, your pick.) Him being a contractor is, in the long run, not the biggest deal to her. It’s him being BK-201 that is a big deal, and even then, canonically? I don’t think she really minds one bit.
Over all I just really like the idea of Misaki/Section 4 working with Li knowing that he is either 1) a contractor or 2) a mercenary who fought in SA per a previous post. Like, they are aware that Li himself has the intentional to be very dangerous, and that he has seen some shit, but they are completely unaware that he is BK-201 specifically.