This portrait is a pair to Hogarth's George Osborne, later John Ranby, Tate Gallery no.T07121. Both have elaborate painted stone surrounds. In Hannah's portrait the surround overlies a more simple oval one, whereas in her brother's the surround was always as we see it today. This suggests that Hogarth reworked Hannah's portrait so that its surround matched the one in the boy's portrait, and therefore that Hannah's portrait was painted first.
Further reading: Leslie Parris
Elizabeth Einberg, Manners & Morals: Hogarth and British Painting 1700-1760, exhibition catalogue, Tate Gallery 1987, pp.204-5, reproduced in colour p.204
Elizabeth Einberg, Hogarth the Painter, exhibition catalogue, Tate Gallery 1997, p.49, reproduced in colour