Mitochondrial DNA is only passed on by mothers.
Nothing saying a neanderthal couldn't be someone's babydaddy...
The DNA sequence of mtDNA has been determined from a large number of organisms and individuals (including some organisms that are extinct), and the comparison of those DNA sequences represents a mainstay of phylogenetics, in that it allows biologists to elucidate the evolutionary relationships among species. It also permits an examination of the relatedness of populations, and so has become important in anthropology and field biology.
Steve Jones's words are .. "For mitrochondria at least, Neanderthals and ourselves split half a million years ago.
I guess that means that we're about 500,000 years away from a female Neanderthal grandmother link.