Neanderthal mtDNA is fairly rare in humans while nuclear DNA is much more common.
Oddly enough in population with higher percentage of nuclear DNA mtDNA is rarer so it’s not clear which side did the gene transferring.
It could be that there are other reasons behind this for example that Neanderthals and modern human female offsprings were less likely to survive or reproduce than males.
But overall it’s really not clear how the populations mixed and who did more of the pillaging and raping.
That's probably more a matter of natural selection. neanderthal y-chromosome DNA was also almost entirely eliminated from the human genome, as well as neanderthal genes in several other places.
When two different dog breeds have pups those mutts are just as fertile as any other dog. When a horse and a donkey have a mule that mule is almost entirely infertile. The first human/neanderthal descendants were probably significantly less fertile than their parents but generations of selective pressure seem to have purged the particular genes that were causing problems which you would expect to include mDNA.
Neanderthal mtDNA is fairly rare in humans while nuclear DNA is much more common. Oddly enough in population with higher percentage of nuclear DNA mtDNA is rarer so it’s not clear which side did the gene transferring.
It could be that there are other reasons behind this for example that Neanderthals and modern human female offsprings were less likely to survive or reproduce than males.
But overall it’s really not clear how the populations mixed and who did more of the pillaging and raping.