Woodworth-Barnes, Esther Littleford and Williams, Alicia Crane, Mayflower Families through Five Generations, Vol 16 Part 1 of 3, John Alden, Boston, Mass.: General Society of Mayflower Descendants, 2002.
According to a couple of sources, Mary's mother was John Alden's first wife, Elizabeth _______. See the Alden source on profile. This same information is in the Mayflower Births and Deaths source if you have access to Ancestry. Another source, Mayflower Families Five Generations (1999) includes Mary with the children of Elizabeth Philips. As such, her mother is uncertain.