@FgoSegul
My guess is:
I think that they (the religious higher ups) are just normal human people, who are attempting to use the Adventurer system in order to spread their influence while expanding their own power / territory in the process. Brand enemy leaders as "demons" and suddenly you have a justification for involving the church. Share some wealth with the nobles, and they will recruit you an army to fight them with, using their own citizens, all in the name of "national defense" or "upholding the Kingdom's honor", or some other bullshit excuse.
All they need is to trick the few strong ones, and the rest will follow. Thus the hero alliance was formed. Now, they may not be idiots (the Heros), but if you set them up with a shitty contract which they felt at the time was reasonable, then you really don't need to worry much about them (like if you refuse to kill the demons, we will kill you for treason, but while conveniently neglecting to tell them that "Demon" is just a pseudonym for "humans who we dislike/are against us, who we want you to kill for us, so we do not need to dirty our own hands." And since at the time it was believed them to be actual monsters, they would have agreed to it without much hesitation.
The nun figured it out, but it is already too late for her, same with the mage who she is dragging around with her. MC was able to be released from his contract under special circumstances though. This causes a MASSIVE problem for the church. Now he is a loose end, which they no longer can justifiably clean up, unless they bullshit a reason, like they did now. Thing is, they actually should not be able to do anything to him, but to try to bluff him into listening to them. They care so much about this because if somehow word got out that the church was just using good people to kill others just for their personal gains, then the church would be rejected by the populace completely, if not entirely burned to the ground (with members trapped inside too).
It is a dangerous ground to stand on if you try to screw over a hero "loved by the public". The public will usually sympathies with the Hero being abused rather than the Hero being the one to refuse to serve the cause. But, if you legally hold their live as collateral so that they will not spread the information, then they can't do much to oppose you, because they simply have to call you a traitor and execute you under that narrative. But if they can't easily get rid of you if you do speak, then that is when they begin to panic.