Hester is indeed using the delivery of the gloves as a pretext to visit Governor Bellingham. Her real reason for going to his home is to plead her case before him. Hester has heard that there are some in the village who want to take her daughter Pearl away from her. Amongst these people, Governor Bellingham has been one of the most vocal, and Hester wants a chance to argue on behalf of herself and of her child.
Governor Bellingham holds "an honorable and influential place among the colonial magistracy, and he has "much power and activity in the affairs of the settlement". Hester has heard that "there (is) a design on the part of some of the leading inhabitants...to deprive her of her child...on the supposition that Pearl...(is) of demon origin". Because of this, they are arguing that "a Christian interest in the mother's soul (requires) them to remove such a stumbling block from her path...(and) if the child, on the other hand, (is) really capable of moral and religious growth and possesse(s) the elements of ultimate salvation, then surely, it (will) enjoy all the fairer prospect of these advantages by being transferred to wiser and better guardianship than Hester Prynne's". In her isolated state, Pearl is all Hester Prynne has, and she goes to the Governor's home seeking an interview with the esteemed gentleman so that she can plead her case before him and convince him to allow her to keep her child (Chapter 7).