They were taken by surprise? Tanya thought they responded to a distress call after the dragon began attacking the magically-protected tower. Presumably the dragon triggered the call and set an ambush.
They took losses and now they're probably feeling it was for nothing and wondering if they could have sat it out for the same result. Well, such are the vagaries of a soldier's life, but Tanya probably should offer them (or the fallen soldiers' families, if they're dead?) part of the prize money if she's to make a positive impression. But she has absolutely no idea how to make the offer in a culturally correct way, or even what amount would be appropriate! Offering someone money for something he regards as his already-paid-for job could be a gift that makes him like her, or makes him feel that he must reciprocate and be annoyed at the unasked-for social debt, or offended because he doesn't need tips, or who knows what!
He's not saying what exactly they saw, but if you ignore the illusions on both sides the actual attack wasn't special in any way, so she sees no reason not to tell him. "I shot him, mostly with explosive bullets. He was invisible at the time, so I don't know what proportion of them he stopped, but they all exploded and from the state of his body later at least one penetrated to explode inside it. I don't know if that tells you anything about his defenses." Maybe Nazir will have some insight such as Ymor... Ymohgr... the dragon doing something at just that moment that required dropping his shields, or that they had happened to weaken them right before Tanya attacked. "Before that, he cast a spell that looked like an electrical discharge, which I evaded; that's why I targeted him. He had several ongoing spells and I don't know what the other ones were doing, I'm not used to the local style of spells." (And probably can't get used to it because she can't change her orb's analyzer, although she can store new signatures.)
"Does not claiming the bounty mean you won't be paid for this mission, or do you have a regular paycheck regardless? I don't mean to be intrusive; the outcome was down to surprise and luck, and you took losses while I paid no cost, so I believe it would be fair to split the bounty between us." This is a gamble, but hopefully it will come across as settling an implicit debt rather than creating one, and as an offer between equals rather than a gift from a superior. Also hopefully, Tanya can parlay this into a longer association so she can get as much information from him as she can before revealing her abilities to anyone else, and make him not inclined to immediately share that information with someone else or use it against her. (Of course she'll ask what he must report to his superiors first, if it comes to that.)
(Sense Motive keyed to Tanya's culture will explain that 'I believe it would be fair' is meant to let him save face and shouldn't be taken literally, although it doesn't mean Tanya doesn't think it would be fairer that way).
How much is a quarter ton of gold coins that she's offering him? How long could she live comfortably on that amount? Tanya has no clue! It would be around 700 thousand marks, enough to set her up in comfort for life several times over. She can't guess at local prices but assuming people aren't taking money to market in a wheelbarrow, how far off can it really be?