Wikitree currently shows the paternal grandmother of Mayflower passenger Edward Winslow to be Catherine Bucke, daughter of Kenelm and Ellen (Neville) Bucke with a lineage going back to royalty and Magna Carta barons.
John G. Hunt wrote a brief article, "The 'Mayflower' Winslows--Yeomen or Gentlemen?" which appeared in NEHGR (1967), 121:25-29. In this article he demonstrates that Edward's father Edward was styled a gentleman, while grandfather Kenelm was a yeoman.
In Part 2 of this article, in NEHGR (1968) 122:175-178, Hunt states the following: "Since publication of the earlier paper on this subject it is needful to reconsider the alleged descent of Governor Edward Winslow from Elizabeth Morgan. Moreover the theory set forth in 1965 that he descended from Kenelm Bucke (died 1550) and his Nevil wife, must be reexamined." Hunt goes on to present the theory that Kenelm Winslow's wife (and the grandmother of Edward Winslow of the Mayflower) was "Elizabeth, daughter to John Foliott, Esq., baptized in 1540 at Pyrton, Worcestershire."
Per Hunt's note, the 1965 theory that Edward Winslow's grandmother was a daughter of Kenelm Bucke appeared in "Clues to the Ancestry of Winslow of Droitwich" in The American Genealogist, 41:168-75, July 1965.
Hunt's "The Mayflower Winslows -- Part III" appeared in NEHGR 182-83, with additional snippets buttressing the theory that Edward Winslow's grandmother was Elizabeth, daughter of John Foliott by his first wife Eleanor Moore.
In any case, there are two separate theories about Edward Winslow's grandmother, so I suppose they should both be mentioned in a paragraph in the bio.