THe identity of Mary Stringer is fairly certain.
The only suitable baptism Mary that has been found gives her parents as Peter and Martha.
They were living in Fakenham too and had several others children born around that time.
Their marriage is the only suitable one for Peter and Martha in Norfolk and this too was at Fakenham.
Her maiden name is given as Laveret in the marriage register. However, the burial of their son Henry suggests that here maiden name was Leveritt.

Baptism serach in FREEREG found only one Marth Leveret (no Laverels at all).
This suggests that her parents may have been Charles and Martha.

A likely burial for Martha states that her husband, Peter, was a Black Smith (written Blacksmith in the Archdeacon's transcript).