As I remember, there is little evidence of Neanderthal jewelry.
As shuckmaster already said above, the estimated date is the reason for attributing it to Neandertal. Neandertal used fabric I think, and passed down genes in any case. The problem of course is that the fossils which are Neandertal are so old, something like a necklace could have been misattributed, overlooked, or left behind beneath the dig.