No petition under § 46b-560 shall be withdrawn except upon approval of a judge or in IV-D support cases as defined in subsection (b) of § 46b-231 and petitions brought under sections 46b-301 to 46b-425, inclusive, the family support magistrate assigned to the judicial district in which the petition was brought. Any agreement of settlement, before or after a petition has been brought, other than an agreement made under the provisions of § 46b-570, between the parent who gave birth and an alleged parent shall take effect only upon approval of the terms thereof by a judge of the Superior Court, or family support magistrate assigned to the judicial district in which the parent who gave birth or the alleged parent resides and, in the case of children supported by the state or the town, on the approval of the Commissioner of Social Services or the Attorney General. When so approved, such agreements shall be binding upon all persons executing them, whether such person is a minor or an adult.