Katherine was not about to get between Klaus and anyone. She did not care who they were. Her entire after life had been spent running from this. As long as Klaus' focus was somewhere else and not on her, she was happy. But Elijah had insisted on going inside to intervene. She would have preferred if he had said his piece while she waited in the car outside. That way no one had a way to harm her, which was the important part of the entire situation.
She stayed behind Elijah as he had instructed and knew better than to say a single word. Instead she kept her grip on Elijah's hand, though she was unsure if it was so he didn't leave her or she didn't leave him.