Small problem; We are not directly related to neanderthals. They evolved as a separate offshoot of development. Gentic testing proved it a couple years ago.
It's better to say they're our cousins once (at least) removed instead of grandparents.
They have not yet sequenced the genome for neanderthal. Once they do, they'll be able to tell if there was any interbreeding.
I'll be the first to tell you that I'm no anthropologist, but what I saw on Nat Geo was extremely interesting...and I did stay at a holiday in express.
Full sequence no. But there been tests which show double the number of different genes than you'd expect for direct descendants.
Think of it this way, somebody checked the floor plan and found that it doesn't match. We haven't checked the blue prints to make absolutely sure.
And yes I know that analogy doesn't cover the interbreeding issue. I couldn't think of one fast enough.