give me some advice

My supervisor was angry with me, because I had a fight with an old lady at other department (she submitted the technical report to general manager without copying to me and I did the most of work, so I was very angry with her). My supervisor did not care about her reporting to GM, he just cares reporting to customers. But for me, I am a new engineer; I do care, but could not report anything, and my manager was unhappy with that. Now my supervisor still thinks that I should not be angry with her, ask me to get well with her, but I refused since the old lady’s nature is so bad. She just wanted you to put efforts, but never give you credit. Should I quit from this project? And How to fix the relationship with my supervisor?