Neither the marriage nor the death record lists her parents. Maybe you could try the CTGenWeb for Thomspon area?
Massachusetts, Deaths, 1841-1915
Alice Towne
Death 17 Jan 1859 Fitchburg, Massachusetts
Female Age: 59 yrs 3 mos 11 days (oct. 6, 1799)
Widowed
Birthplace: Thompson, Ct.
Spouse's Name: Abial J. Towne
Reference ID: v 131 p 110
GS Film number: 960175
Massachusetts, Marriages, 1695-1910
Name: Abial J. Town
Spouse Allice Bates
Marriage 21 Feb 1819 Event Place: Bellingham,Norfolk,Massachusetts
Indexing Project (Batch) Number: M50014-1