The girl in question was Lucy Mancini, Sonny's paramour at Connie's wedding, and later his mistress when he and his guys are "on the matresses" during the Five Families War of 1946. The novel has a subplot involving Lucy and her lover, Dr. Jules Segal, physician at the hotel that Moe Green owns and where Freddy Corleone is in training (and getting slapped around). Jules advises Lucy to get her insides tightened, having had his attention drawn to her condition after making love to her. And he's present at her operation. Jules also arranges for one of his surgeon pals to fix Michael's face.
This was a fairly interesting subplot in the novel, but in my opinion, Puzo included it so he could go into detail about Lucy's operation, repeating some medical facts that he'd picked up somewhere (just as he went on and on about Hollywood practices in "The Last Don." I think FFC was right not to include the Lucy/Jules/Vegas/operation subplot in the film.