She wants to protect Iruma, and nothing more
She definitely want to protect Iruma, but she should be able to keep her cover too, so long as the other guy don't hoe her.
The main plan is to find stuff that belonged to the Missing Demon King, capturing Iruma is just a bonus objectif, in the specific case that Iruma is the one finding out.
Since here, the guy is the one going completely off board, she can beat him up just enough to get reputation points while allowing him to escape, ence increases her chances of completing the mission.