He nods to her and picks up his Acts to page through, praying.
It would have been straightforward if she had mentioned, first of all, that she had this need, and had suggested that he adopt a general policy which would only incidentally cover her. He would probably have agreed that it sounded like a good policy if it's a thing people were likely to want. The fact that she is clearly threatening to kill him makes it harder, not easier, to adopt this policy; now he has to figure out whether his preference not to die is contaminating his application of Law.
He doesn't really care about the money. It can presumably be used to buy things but only things that people happen to bring by his church, at least until such time as he has somebody willing to run errands to and fro, and if someone happens to bring a thing by his church, he can barter for it with spells. He would really have made a terrible Abadaran, wouldn't he. So at least the money is not contaminating his application of Law.
He expects that properly competent Iomedaeans can promise confidentiality. Iomedae does it sometimes, in the Acts. He knows slightly more about how Abadarans do it because he has been responsible for enforcing rules protecting Fiducia Boian's offers of confidentiality to let his men report anything they thought might be a safety issue with the fort. It was important to be able to offer that, because ultimately they were allied toward the goal of holding the Wound, with the subgoal of the fort functioning: not just Blai and the Fiducia, but anyone who might have chosen to report, and anyone who might have formed the suspicion that they were being reported on, all benefited from this being possible. Are he and Para Bellum allies in any important way? Clearly not in very many important ways. More thoroughly allied parties would do this in the correct order. If they failed to do that, maybe because they were brought by friends while unconscious and the friends didn't understand the need, they would... well, it might depend on the strategic picture. It does at least suggest that Para Bellum does not perceive herself to be allied with Blai if she is moved to, rather than go into more detail on what she needs and why, resort to treating him like a single-use healing scroll to be disposed of once deployed.
If she had been brought unconscious... let's say by a nonspeaking summoned creature who thereafter went back to its own plane, to avoid the loose end in the hypothetical... then he would have healed her, and would not have the nagging concern that she ought to have gone about this more professionally. It seems to be a feature of his aims in establishing this badlands church that he would like to be able to take in and heal people without needing to know much about them first. He wouldn't have demanded to know her identity or have a look at her more distinctive possessions, if she'd arrived in disguise, or if he'd been alone without someone who could recognize her. So it - well, now he's back to thinking that she didn't go about this very professionally. But he isn't trying to be solely a healer of professionals.
The policy she proposes is Lawful and he thinks he would have accepted it without duress. A lot of Law is about being able to do things out of order, a little bit; to time travel, a little bit. He can go back to himself before her arrival, and tell him to adopt patient confidentiality, and then it's solved. The puzzle completes neatly that way.
He shuts his book. "Your patient confidentiality idea is good. I will do that. You do not need to pay me to do it. I will do it for everyone now."