In Dragon 95 (p 12), Gygax says that Bombadil was his favaourite character from LotR:
The Professor drops Tom Bombadil, my personal favorite, like the proverbial hot potato; had he been allowed to enter the action of the books, no fuzzy-footed manling would have been needed to undergo the trials and tribulations of the quest to destroy the Ring. Unfortunately, no character of Bombadil’s power can enter the games, either — for the selfsame reasons!
It seems pretty well documented that clerics, including their power against undead, has its origins in a vampire hunter in Arneson's game.
But at a certain point, the clerical ability was generalised from an anti-vampire power to a general anti-undead power. Who did this?
It seems possible that Bombadil's example of driving away the barrow wights was one of the examples that Gygax had in mind if he was either involved in that design, or going along with its inclusion in the design after it was put forward by someone else (eg Arneson).
When Caliburn101 reports that Gygax described Bomdadil as
the model for clerical turning, I don't know how much weight is meant to be placed on those exact words. Perhaps Gygax meant that it was
a model, or was one of the exemplars D&D players might draw upon to make sense of the ability within the game, or was something that he, Gygax, had in mind in "allowing" the ability into the game.