She was not in a hurry to do anything.
It seemed that the King not only summoned her for a medical checkup, but also summoned Gu Ruxue, who was supposed to be the Phoenix Girl. Such a big accident happened in the court, it was very normal for the King to want to see the Phoenix Girl to calm himself down.
Gu Ruxue had no idea why she was summoned here, so she snapped at her.
Gu Chaoyan was not in a hurry, but waited for the King to speak to her.
Gu Chaoyan had noticed previously in the wing-palace that the King was very afraid of being killed. She was summoned to check him up because he needed her desperately.
Therefore… he was not going to allow Gu Ruxue to drive her away.
The King did not like her, but could not do anything about her. So he was making Gu Ruxue give her a hard time first, but Gu Chaoyan wasn't afraid of any of these. She seemed quite calm.