She died in November 1808 in Farnworth. Her burial was on November 6th, 1808 in Farnworth.1
Death Notes
This cant be Elizabeth, as Peter died 1789. Also this Betty is of Deane, so would not be buried at Turton: Name: Betty Mather Event Type: Burial Burial Date: 25 Jul 1774 Parish: Turton, St Anne Reference Number: GB127.L98/1/2/3 Text: "Betty Mather of Turton, Widow"
I've read through the St Mary Dean burials and there is no Betty Mather, or wife of Peter Mather, or any other Mather of Little Hulton that died soon after these 2 children, so the Peter that married Ellen Howarth in 1762 must be another.
If Betty survived Peter then she may have remarried Thomas Halliwell in 1792. A Thomas of Farnworth died 1806, and Betty died 2 years later. This appears to be a good fit.
Name: Betty Halliwell Event Type: Burial Burial Date: 28 May 1809 Burial Place: Deane, St Mary, Lancashire, England Parish as it Appears: Deane Reference Number: GB127.L85/1/4/2
Name: Betty Halliwell Event Type: Burial Burial Date: 6 Nov 1808 Burial Place: Bolton-le-Moors, St Peter, Lancashire, England Parish as it Appears: Bolton Abode: Farnworth (see both images) Reference Number: GB127.L243/1/2/3.
There is a Betty Mather from Edgworth who died Apr 1817m aged 85 (born 1732) and buried at Turton. This could be her too.
General Notes
After husband Peter died in 1789, Betty would most probably have remarried. The most likely match is a marriage 18-Dec-1792 to Thomas Halliwell, a widower (although Betty Mather is recorded as a spinster).