What idea is Nathaniel Hawthorne suggesting through the character Pearl in "The Scarlet Letter"? How does she change throughout the novel?

Pearl, as an illegitimate child, exists outside of the Puritan community; having no acknowledged male in her life, Hawthorne has the Puritan community refer to her as the “the demon offspring, the elf-child,” and she is characterized as revolting against that community (refer to the description of her playing in the woods) and mimics her mother’s ostracization by making her own “scarlet” letter A. She serves to remind Hester and Dimmesdale of her error, and serves also as Chillingworth’s impetus to exact revenge. At the end of the novel, her transformation occurs when she is publicly acknowledged by her father Dimmesdale. “Pearl kissed his lips. A spell was broken... [she would not] forever do battle with the world, but be a woman in it.” Hawthorne continues to explain that with her inheritance from Chillingworth, she “became the richest heiress of her day in the New World...she might have mingled her wild blood with the lineage of the devoutest Puritan of them all.” Thus, she transforms in the community’s estimation from social outcast to the most esteemed, suggesting that “all is forgiven” when there’s an estate at stake. She and her mother retire to England after the minister’s death, where presumably Pearl marries, has children, and enjoys a fulfilling life.