In chapter 26, when Scout tries to talk to Jem about Miss Gates she mentions the courthouse. Jem grabs Scout and tells her never to mention that courthouse to him again. Jem is still very upset about what happened to Tom Robinson. He believed that the jury would find Tom innocent because Atticus proved that he did not hurt Mayella. Jem's innocent outlook on life was stolen from him that day and he has yet to deal with it emotionally. Atticus tells Scout, "don't let Jem get you down."
When Scout tries to tell Jem about Miss Gates (her teacher), Jem reacts violently because he is mad and upset that Tom was wrongly accused and convicted of raping Mayella Ewell. Speaking of the trial makes him very mad and sad, so he does not like talking about it.
The correct answer is "her". This is because an antecedent basically means to whom does the pronoun refer and the pronoun has to refer to Miss Kensington. This is why the correct form is her.
