Early in the story, after Dexter's winter daydream of becoming golf champion, he decides to stop caddying because he is too old. Fitzgerald implies that Judy Jones is at least part of the cause of his quitting with the paragraph beginning, "The little girl who had done this was eleven--beautifully ugly as little girls are apt to be who are destined after a few years to be inexpressibly lovely and bring no end of misery to a great number of men."
Dexter is fourteen and this is his first encounter with Judy. Although Judy was so young, he foresaw that she would be very beautiful in later years. When the caddy-master demands that Dexter pick up Judy's clubs and caddy for her, he definitively quits because such a gesture (possibly in defiance of the adults and an alliance with Judy) felt necessary after his encounter with Judy. That is to say that Dexter felt he needed to quit because of the "strong emotional shock" he'd just experienced.
Nine years later, (Part II) while golfing with Mr. T. A. Hedrick, Mr. Sandwood, and Mr. Hart, Judy hits a ball behind them that strikes Mr. Hedrick in the abdomen. Later that afternoon, Dexter sees Judy while he is swimming. She asks him to drive her boat so she can ride behind on a surf board. He complies. She asks him to dinner and he accepts. Dexter soon realizes that he must compete for Judy's attention with other men. He finds himself in a position of being Judy's shoulder to cry on as well as a potential mate. Having all these men to choose from, Judy alternately encourages and discourages Dexter. He eventually finds another girl: Irene. (However, this would not be the end of his infatuation with Judy.)