Why do you think Meg finally trust the beast?

Aunt Beast telepathically spoke to Meg using kind language, the creature felt safe.

"While Meg thought, the beast murmured to her gently. "No, mother is a special, a one-name; and a father you have here. Not just friend, nor teacher, nor brother, nor sister. What is acquaintance? What a funny, hard word. Aunt. Maybe. Yes, perhaps that will do. And you think of such odd words about me. Thing, and monster! Monster, what a horrid sort of word. I really do not think I am a monster. Beast. That will do. Aunt Beast."

While IT used his mind to control, Aunt Beast used her mind to comfort and communicate.

Meg feels very safe and loved when she is with Aunt Beast. Aunt Beast is extremely comforting with Meg and makes all of the bad things in her life seemingly go away. Aunt Beast is like a mother figure to Meg and makes her feel very happy, since Meg has gone on this journey without her mother, having this nurturing creature around her makes her feel safer.