I received a Geni message pointing me to Find A Grave which claims that this woman, mother of Elizabeth Greene, was Agnes Rucke Wright.https://www.findagrave.com/memorial/109870471/agnes-wright.
I took a quick look on the Internet but couldn't find any reliable discussion of Elizabeth Greene's ancestry.
Does anyone who is good with Medieval sources know how to verify or refute the Find A Grave claim?
Be very careful, the Medieval Greene’s have a lot of bogus ancestry.
The way to verify is to go down the tree to the immigrant ancestor. Then we can find peer reviewed articles on his / her origins.