General Notes

In the "Parish and Probate Records lists for year 1679 (during the persecution)", it states that a "Thomas Grimstone and Mary Squire not to be found."  They were apparently "nonconformists" who had fled.  Another listing shows the marriage of a John Squire and Mary Hoard.  These people may or may not be related to THIS Mary Squire, but it is worth keeping in mind that they were around in the era of the persecutions.
"Devonshire England Parish and Probate Records (Parish Registers and some Bishop's Transcripts at Wells)" records the burial on November 18, 1629 of a "Mary w. of Richard Squire."  They may have been close relatives, but I have not confirmed this.

OTHER SOURCES: LDS familysearch.org IGI CD#28 Pine #941282--contributor: Norma J. Burgess, Great Falls, MT 59404), and "Yorkshire: Northowram, Coley--Nonconformist Register, 1644-1752".