All this chatter about the viability of offspring of different pairings is all very interesting, but people are overlooking the social aspect to all of this. Mitochondrial DNA is passed down from mother to offspring so there needs to be an unbroken line of daughters for there to be modern Sapiens with Neanderthal DNA. But think back to the first hybrid offspring of that Neanderthal mother - it would have most likely stayed with the mother and her social group, so you are more likely to find hybrids with Neanderthal mitochondrial DNA in the Neanderthal population. Hybrids in the Sapiens population would be more likely to be the offspring of Sapiens mothers and Neanderthal fathers. For there to be Neanderthal mitochondrial DNA the Neanderthal mother would need to be socially integrated into the Sapiens group. Maybe someone more knowledgeable than me can say if there’s any archaeological evidence for this. But it seems likely to me that these were “one night stands” (allow me to be anachronistic haha) rather than “marriages”, otherwise Neanderthal mitochondrial DNA would be part of our modern genetic diversity.