If Yao Jing didn't apologize, Ye Jian would probably have laughed off the matter and wouldn't take it to heart.
But she stood up to apologize and did not say anything similar to her mother about forgiving herself. This showed that Yao Jing was shrewd and scheming.
She knew that she had to apologize immediately for doing something wrong and not delve further into the mistake or repeat it again and again.
She knew that she was in the wrong and apologized. It didn't matter if Ye Jian accepted her apology or not, as long as she had apologized, even if Ye Jian was angry, she would not be in a favorable position to cause trouble for Yao Jing.
Ye Jian won't be causing trouble for her. Otherwise, it would seem that she's narrow-minded.