Is it possible, since Philippa's parentage is in question, that people are confusing her with Philippa l'Arcedekne (who was married to Sir Hugh de Courtenay)? I found a Philippa listed on The Peerage, and they cite Burke's peerage: http://www.thepeerage.com/p921.htm#i9201
This seems reasonable, and might explain all of the questions regarding Philippa.
There is a WikiTree profile (albeit lacking) for Philippa l'Arcedekne Arcedeckne-9
(Edited to add the following):
There is also a Philippa Grenville listed (connected, with no profile information about spouse, etc.) as the daughter of Sir Thomas Grenville and Isabel Gilbert (found on The peerage, which cites L. G. Pine, The New Extinct Peerage 1884-1971: Containing Extinct, Abeyant, Dormant and Suspended Peerages With Genealogies and Arms (London, U.K.: Heraldry Today, 1972), page 9. Hereinafter cited as The New Extinct Peerage- whose co-author is Burke. The Peerage lists this Thomas Grenville as "Sir Thomas Grenville, son of Sir Thomas Grenville and Elizabeth Gorges.": http://www.thepeerage.com/p2571.htm#c25709.1
This Philippa married (according to the peerage) "Philippa Grenville was the daughter of Sir Thomas Grenville and Isabel Gilbert.1,2 She married, secondly, Humphrey Arundell, son of Thomas Arundell and Catherine Dynham.1 She married, firstly, Francis Harris.1 She died in 1524.2
Her married name became Harris.1 Her married name became Arundell." ([S21] L. G. Pine, The New Extinct Peerage 1884-1971: Containing Extinct, Abeyant, Dormant and Suspended Peerages With Genealogies and Arms (London, U.K.: Heraldry Today, 1972), page 9. Hereinafter cited as The New Extinct Peerage. [S130] Wikipedia, online http;//www.wikipedia.org. Hereinafter cited as Wikipedia.)
I asked the question/s on the profile, but figured it was good to post here as well, so that it reaches more people (instead of reaching just the profile manager).