While Claire might not know completely about her Arcana, she at least knew that Agatha is originally a Celestial grade and had a part of her strength being sealed away by Archangel Michael himself before she awakened as Claire's Arcana.
From the divine sword spirit, she also learned a little bit about Celestial grade spirits. Unlike the lower grade spirits, their memories won't be erased even after rebirth.
Agatha is the one that gave her hope of defeating Leah in the future once she makes a breakthrough to the Exalt realm and breaks the remaining seal to unlock her full potential.
It is the reason why she felt Agatha must be right if she was forced to use such powerful techniques against a human. Her negative feelings for Estella made her think that she deserved the punishment too.