No deaths for Mary Mather recorded at Tameside, Manchester or Ashton under Lyne (where brother Joseph was recorded).
The Mary Mather of Fern Street, Bury that died in 1920, aged 63 with Will was a widow, so not this Mary. Lancashire Death indexes for the years: 1920 MATHER Mary 63 Turton, Bolton TUR/21/163
General Notes
In 1861, Mary (4) was living with her grandparents Joseph and Betty
In 1891, "Maria" was 33 and head of family at Droylsden with brothers Joseph (31), Daniel (28), and sisters Ann (24 and Betsy J (17)
In 1901, Mary (43), was head of household, born Dunscar, Turton was living with Joseph (42) and Ann (34) in Droylsden.
In 1911, Mary and borther Joseph (53 & 53) were living with their sister Ann and John H Bently (45 & 39). Mary never married.