once again the mindset of all these kids is ridiculous. to not treat an escaping prisoner as such immediately but instead allowing her to participate in your closed-off community, potentially getting some real intel about your group and even allowing a duel to happen which might just cause massive damage to the few mechas they had available, is just crazy. and she could have tried to escape if she could have started the mecha up which they didn't seem to consider at all. and then they bring her to the bank, where, if she had decided to explain the situation to the bank officials, she could have found a means to escape, since banks tend to be neutral ground, and upon realising she's treated as "legally dead", she just accepts it and instantly thinks about offering her body (is how i interpreted that short panel) but instead accepts to work her debt off.
this is one series where kids kill kids and adults without any second thought, so i guess i'm simply expecting too much depth.
I would say that you probably are indeed expecting too much of this, but that aside, I feel that you don't remember that they - despite having a particular purpose - are a mercenary group. They don't have secrets to hide in the way a nation does.
And can she "explain" away the situation to the bank so easily? She can tell them whatever, but can she
prove any of it in the current situation? Any scam artist/thief could have the same story. Furthermore, even if the bank fully believed her, what does that change? The death declaration isn't something a bank can overturn, because they're just a bank. The account is closed already, the funds removed (it should be in the hands/account of her family).
No matter how you think about it, she needs to go home to fix that. And if she was even a little smart, she'd be explaining that to them. She should tell them: "bring me home, so I can straighten out that I'm alive, get money to pay what I already owe you, a little extra for transporting me, and I can easily convince my nation to hire a strong group like you guys too."