A paper by Morin Laroulandie  suggests that Neanderthals wore ornaments made out of eagle talons. The evidence is that there are some very strange cut marks onthe upper part of some raptor talons found in association with Neanderthal sites.
The cutting is what would be expected if the talons were to be removed from their sheaths.
As thes marks are only found on eagle talons and this happens at different sites and is spread out over a very long period of time... it seems that they used the talons for some reason. The authors write:
Although the sample size is small, the fact that all the terminal phalanges that show cutmarks are from eagles argues against their utilization in strictly non-symbolic contexts. This last pattern is noteworthy because eagles are among the rarest birds in the environment, a pattern explained by their high trophic position in the food web.
This bias toward large and powerful diurnal raptors possibly indicates that the claws were used in symbolically-oriented contexts by Neanderthals, although the latter contexts remain to be more precisely defined. One possibility is that they were used as ornaments...
So if we find these talons in America, then we could suggest (if their age is appropriate) that they were of Neanderthal origin.
Eagles in Mesoamerica
Regarding the "context" mentioned above, it is not too surprising to find that eagle talons had a place in Aztec magic rituals .
They even had a special name, Cauhtetepontli, (actually applied to the whole claw), the talon itself was used during birth to assist women and protect them and the child. The talon is a symbol of victory of man over the forces of nature.
I cant tell if this is a myth that came from Neanderthals and was taken up by modern humans or was created separately by them. But it is interesting.
 Morin E , Laroulandie V. (2012) Presumed Symbolic Use of Diurnal Raptors by Neanderthals. PLoS ONE 7(3): e32856.doi:10.1371/journal.pone.0032856
 Carlos Viesca and Ignacio de la Peña La Magia en el Codice Badiano pp.275.
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