That's why the only thing I could tell her since we had quarrelled was: "It serves you right, I'll hate you for the rest of your life!"

quarrelled 是动词 quarrel 的过去分词形式。quarrel 的意思是"争吵、吵架"，指两人之间发生激烈的言语冲突。过去分词 quarrelled 在这里表示"已经发生过争吵"的状态。