William is most likely the s/o William Terrey and his wife Joan
William Tery and his wife Margy may have been born about 1500.
I suspect they are the parents of the parents of Joan Terie (born about 1534) who married married Henrie Dennisse in East Peckham on Feb 15 1559/1560 because:
We principally know them from the following real East Peckham estate record.
East Peckham: Henry VIII year 38 (between 22 April 1546 & Jan 1547) item 2496. Wm Terry & wife Margy to Wm Mowseherst. 7a land, 5a mead & 12a past in E. Peckham. £30.
I suspect Margy is the "Mother Terrye" who was buried at at St Michael's East Peckham on March 31, 1562. if so they may be the parents of Joan Terie (born about 1534) who married married Henrie Dennisse in East Peckham on Feb 15 1559/1560. In his will, Henri says he was a yeoman.