Edith was a sister of my ancestor William Cromwell who came to Maryland with his brother John in 1667 from England. She is not a daughter of Oliver Cromwell although there is a claim of the family to Henry, son of Oliver. Another claim I saw was to a brother of Oliver. But there is no proof.
About 1680 a younger brother of John and William, Richard, came with his sister, Edith, to Maryland. According to Mr. Newman, Edith soon became the bride of Christopher Gist, explorer, and the g-grandmother of Mordecai Gist of Revolutionary War Fame.
As to the claim of the family to Henry Cromwell, son of Oliver, it is noted that the given name of Henry is conspicuously absent in all lines of the Maryland Cromwells. Francis B. Culver, an eminent genealogist, emphasizes this point some of his research and suggests that such a name as John, William, Richard, Philip, Joshua, and Edith were all associated with a family of Cromwells from Malmesbury, Wiltshire, England.