If a Bas Levi has a son with a gentile, the son does not need a pidyon haben. In the case of a daughter born between a Bas Levi and a gentile, is the daughter of that union a Bas Levi or an Yisrael? If she were to have a first born son, would he need a pidyon haben?
You're asking about a grandson of a bas levi? This only works one generation; it's not an "any drop of blood" thing.
Miss Levi marries Mister Israel; their firstborn son doesn't need a pidyon haben because he was born to a Levite, and the Torah uses language of "first out of the womb" -- and the womb, in this case, is Levite. However, their child, Baby Israel, is 100% a plain-old Israelite, as tribal identity is patrilineal. The exemption is not because Baby Israel is part-Levite, but because he was born to a Levite mother. Same thing if Miss Levi and Mister Israel have a girl -- let's call her Sarah Levi-Israel; when that girl grows up, her children, assuming she married an Israelite, need pidyon haben because Sarah's father is an Israelite.
(This is, by the way, a common mistake; I know a fellow whose bas-kohen maternal grandmother, remembering her own son, insisted that the 100% Israelite grandson didn't need a pidyon haben -- mistakenly. The fellow realized this years later and had to do his own pidyon haben.)
None of this really changes if the father wasn't Jewish -- the child halachically has a Levite mother, and halacha recognizes no particular father -- the child is basically an Israelite with subprime pedigree for those snobbish about such things. There's no "Levite blood" that halachically would affect a future generation.
(Before arriving at the follow-the-womb logic, the Gemara Bechoros 47a entertained a possibility that the product of a Levite mother and non-Jewish father was more um, Levitic than if the father was an Israelite ... but once the Gemara reaches the follow-the-womb explanation -- and we follow it, per Tosfos s.v. mar berei pointing to Chulin 132a -- it appears we reject that as practical halacha.)