Because she can see through any reflective surface, and he's really paranoid. Even if you covered it up, he'd probably see you as a liability or something. His patron hates ours, too.
[handwaves]
I'm not going to tell you if you should or should not. If you want to officially make a pact with Mirror, that's fine, but you aren't really gaining or losing anything from not doing so. If you want to have Scowl's trust, don't.