Douglas Ricardson states that Ralph de Arundel was a "probable illegitimate son" of Richard de Arundell, Knight, Earl of Arundel and Surrey, by an unknown mistress. Richardson explains his reasoning in a footnote, [2]
In assigning Ralph de Arundel as a son of Earl Richard de Arundel, Richardson states, [3] "The arms in question (Arundel and Warenne quarterly) were brought into being in 1347, when Richard de Arundel, Earl of Arundel (died 1376), became heir to his uncle, John de Warenne, Earl of Surrey."
From the date of the origin of the arms, Arundel and Warenne quarterly, Richardson concludes that Ralph de Arundel can only have been a child of Earl Richard de Arundel or of one of Earl Richard's siblings. Richardson quotes Montagu's discussion, but notes that the earl is known to have had an unhappy first marriage and to have fathered at least one other illegitimate child. Richardson also suggests that the fact that Ralph bore the surname Arundel is "evidence that his father was an Arundel, not his mother, as bastard sons in this time period usually bore the surname of their father." [4]
[2] [3] [4] Douglas Richardson, Plantagenet Ancestry, 2nd edition, 3 vols. (Salt Lake City: Douglas Richardson, 2011), 1:278,

Presumably daughter of William de Grenville, by his wife, Christian. They had one daughter, Alice.