If the Neanderthal carried off a Cro-Magnon woman it would make no difference to the Cro-Magnon gene pool (or the modern human gene pool) because any child that the Cro-Magnon woman had would then be in the Neanderthal community and 100% of Neanderthal communities went extinct along with any intermixed genes that were over in them.
And, I will make this point yet again. Humans are extraordinary in their willingness to have sex with non-humans, and even amongst humans it is an extraordinary willingness. There is not the slightest evidence that a Neanderthal would even imagine having sex with a human. There is this inescapable tendency, I think, because of the great morphological similarity, to 'anthropomorphize' Neanderthals. Perhaps it sounds odd that I even object to this, but the animal kingdom is replete with very similar animals that have very different behaviors.
Let me give you an example: Dolphins. Bottlenose dolphins happen to be one of the extraordinarily rare species, such as humans, that will have sex with other species (a dolphin will have sex with a human, for instance). No other cetacean will.
Species after species after species will not have sex with closely related species even in cases where they would produce progeny - a moose and a cow for instance. In most cases, even closely related species such as cows and yaks will produce hybrid progeny that are only viable for about two generations before fertility attenuates below propagation.
This assumption that Neanderthals were nothing but humans with a brow ridge is utterly and totally absurd IMHO. There is simply no basis whatsoever for the idea that a Neanderthal would consider mating with a human; could even speak any intelligible language, much less the Cro-Magnon language; could produce viable hybrids, and hybrids that maintained fertility over multiple generations; or would find anything remotely attractive about a Cro-Magnon.
And then you get these tendentious "reproductions" which are nothing but more conjecture. So you have that red-haired Gibraltar girl above, quite obviously intentionally made to look as human as possible, with her sloping forehead concealed by a fictitious shock of hair (their hair was probably limp and greasy), with no discernable brow ridge to speak of, with no characteristic Neanderthal nose to speak of, and with nice pretty eyes and freckles to boot.
And we don't know if that even remotely resembles an actual Neanderthal. It almost certainly does not.
I could go on and on, but I am content with the mtDNA evidence because that's the best evidence we have to date. And not just that, but a glaring big huge elephant in the room: No mixed communities in the archaeological record, and a swift vanishing of Neanderthal communities almost exactly whenever the Paleolithic humans came along into an area.
Hmm.. "anthropomorphize" was a bad choice of words; "humanize" works better I think for what I'm trying to convey.
I don't think interspecies sexual contact is at all unusual or even remarkable. I myself have seen dogs try to mount just about anything that moves. My sister had a llama that she had to have castrated because it kept raping her sheep. Stories of moose mounting cattle are common and hybrid species like mules, ligers, pixie-bobs and beefalo are not terribly unusual. If you google "world's worst hunting dog" you'll find a variety of pictures of dogs being mounted by wild animals.
The common factor in all these cases are males that are more horny than they are particular and there is no reason to believe that Neanderthals were any different. In any event, we aren't talking about two wildly divergent species. If you were to see a Neanderthal walking down the street today dressed in modern clothing you might not even notice him. Heck, there's even an outside possibility that there might have been a sexual attraction between the two groups. That seems to be the case today with white men and Asian women and black men and white women.