I take it Mary is this one
and the one at the bottom of page 88
which thinks it was her uncle not her father who married Katherine Neville.
Burke’s Landed Gentry, to which I do not have immediate access, is cited at http://knight-france.com/geneal/names/677.htm as giving John West as the only son of Leonard W and Barbara who did not die young - and at http://knight-france.com/geneal/names/671.htm as stating that John W married Mary Throckmorton. The History of Parliament Online website says the name of Mary’s mother is unknown and that it was her uncle Clement who married Katherine Neville: http://www.historyofparliamentonline.org/volume/1509-1558/member/throckmorton-kenelm-1514-8387 and http://www.historyofparliamentonline.org/volume/1509-1558/member/throckmorton-clement-1515-73.
Katherine Neville appears to have two profiles on Wikitree - https://www.wikitree.com/wiki/Neville-302 and https://www.wikitree.com/wiki/Neville-2208. The second of these just has a FamilySearch source. I have just checked the FamilySearch source for the second profile, and things on FamilySearch have since been amended so that Katherine is now given as the wife of Deodatus, otherwise known as Clement, Throckmorton, who is clearly the same person as Clement Throckmorton MP. That marriage relationship accords with the other sources. See https://www.familysearch.org/tree/person/details/KZYV-VS8?1=1&spouse=2671-WQH.
As so often, there seems to be tidying up to be done! Throckmortons are not a family whom I have studied, but should we merge the 2 Katherine Neville profiles and go with her being wife of Clement?