John Griswold of CT. & Rome NY

I know that a young Private John Griswold of Ct. married Polly Starkey, daughter of Timothy Starkey and that they moved to Rome Ny. One of their daughters, Mary, married William Thompson, a Scotsman. They moved to Pine Grove PA. where both are buried. I want to find proof that the Mary who married William is in fact Johns daughter. I suspect that the G. middle enitial of their son John G. Thompson stands for Griswold. This has been very hard proof to find for some reason. Can anyone help?