The kobold pauses, briefly, in a you-have-made-a-misstep sort of way. "They're not likely to be involved in this."
She's trying not to let this come to the fore, but it's still there, if muted: She cares, fiercely, about this person. Not because she's getting something from them, not because it's someone she trusts, or finds likable, or enjoys being around; actually, almost because she's not, and doesn't. Because everyone needs to be cared for; because the people it's hardest to care about are often the ones who need it most. Because you don't just give up on people. Because you can only get to the point of everyone being okay if you care about everyone being okay.
And she doesn't trust the Jedi to be on board with that: Here's the warriness of someone who knows on a very personal level what it's like not to be on others' priority list at all, in terms of being okay; she's not concerned for her own self, here, now, with that, but it's still a very personally important issue; not the most important one, but not something she'll be budged on easily. At the same time, there's a sort of detachment: It is correct to care about people and want good things for them, and she wants the Jedi to do that, but in something like the sense that one might want good weather; there's nothing she can actually do about it, and she fully accepts that she's going to have to work with whatever reaction they have; the unwanted reaction will limit her options, perhaps sharply, compared to the wanted one, but she's fully ready to accept that if it happens. And from another angle: Even with all the resources she and the Jedi can bring to bear in the best case, and no matter how much she wants it, it might not be possible to arrange for that person to be okay, or it might not be possible without harming other people; she's not ready to give up yet, but she knows that she might come to a point where she needs to, and she won't hesitate to if she finds herself there.
And then she tucks that whole knot of emotion away, neatly; it's clearly a practiced shift, from that to focused productive diplomacy. "But I can tell you a bit about how we met, if you'd like; that'll also give you a better idea of some of the resources I might be willing to offer."