She was apparently from a family which had lived on Cape Elizabeth for some time; according to S36, "more Dyers are shown participating in the [Revolutionary] War than any other family in the area" (1).
I'll be darned if I can find her parents, though, and she in fact appears as a "lost Dyer" on the best Dyer family forum on the web.  There is much literature out there on the Dyers, but I've found no good leads on her parentage specifically. The list of Ephraim Clark's marriages does not say that she was a widow when married, and this is noted in other cases.
How might she be related to the family Anna Dyer, wife of Samuel McLellan? Many Hannah Dyers appear in Underhill, The Descendants of Edward Small, including the Anna Dyer who married Capt. Samuel McLellan, but not this one.
Little discusses a Dyer family which seems a likely possibility, since he leaves lots of loose ends, but Hannah is not included.
There is a Jabez Dyer, "formerly of Cape Elizabeth,", m. Lydia Dyer, with children Jordan, Hannah, Jabez, Jr. 
Other. . This has a series of Dyer family studies in it.
More references. 
There is a Dyer family in Cutter, but I don't see her there. Cutter focuses on Massachusetts, Rhode Island, and Connecticut. [4, 5]
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Hannah is 17 degrees from Charles Grey, 18 degrees from Henry Herbert, 26 degrees from William Cobbett, 19 degrees from William Lamb, 26 degrees from James Lush, 21 degrees from David Heath, 20 degrees from Mary Ann Withers, 23 degrees from Robert Blake, 38 degrees from William Dove, 29 degrees from Richard Venfield, 27 degrees from James House and 19 degrees from Karen Stewart on our single family tree. Login to find your connection.