She was his second wife. Also, she may have been Mary Lippitt Barlingstone, widow of William Barlingstone who drowned in the Bay about six weeks after their marriage March 23, 1661.
According to the Burlingame Manuscript by Nelson Burlingame (1986), Vol. 1, pg. 8, Mary's will was dated March 6, 1719 and proved Feb. 3, 1720. The Executor was her son Moses. The will reads: To son-in-law Thomas Burlingame & wife Martha,