The Watch Tower Society doesn't seem very sure what to say about Neanderthals. Neanderthals haven't been mentioned in The Watchtower since 1964!
In other publications, their approach has been to completely ignore the time period of Neanderthals and instead focus on similarities to modern humans.
Even then, they just keep wildly stabbing in the dark.
*** lf Question 4 p. 28 Has All Life Descended From a Common Ancestor? ***
Question: Is brain size a reliable indicator of intelligence?
Answer: No.
*** g81 6/22 pp. 14-15 Were There “Cavemen”? ***
NEANDERTHAL MAN is also one of the better-known parts of the so-called evolutionary chain. When the first skull portion was found one scientist called it the skullcap of an idiot. ... And rather than his being an idiot, it is now admitted that Neanderthal man had a larger brain than most modern men!