"Then keep your secrets, it's fun cracking the truth on your own." It was apparent, that he was never going to get any direct answer from this woman unless, of course, he agreed to go with her and join whatever shady organization she was part of.
Hence, the reason, Amir showed no direct interest in her words. If she wishes to tell, then she will, otherwise, he let go of the issue.
Besides, although the Butler was weird in his eyes, he wouldn't harm him, that's for sure. While she can't say the same for the mysterious woman in the mirror.
"You are no fun.' She said, before saying goodbye and disappearing altogether.
But her departure didn't mean that Amir had forgotten about her words. 'Even their master warned them against Burghim… who is he?' For one, it would be good to know who the master of the Woman in the Mirror was. This way, he can somewhat ascertain the danger value of Burghim. And how to handle him.