There is no "orc mythology." Although the term appears in two Anglo-Saxon texts (in two different forms), these are obscure references, which do not indicate a belief in a unique species of supernatural (or otherwise) beings as appears in Tolkien's novels or has subsequently been adapted by every following expression of fantasy worldbuilding that borrows from Tolkien.

Tolkien invented the orcs as a type of creature that opposed his forces of good in his novels. They are his literary invention. There is no indication that Tolkien invented orcs as a reference to Neanderthals.

In addition, there are no expressions of European folklore of any sort (setting aside the literary orc) that can be linked to any folk memory of encounters with Neanderthals - despite the wild conjecture of some people who have license to imagine all sorts of unfounded things, putting forward their speculation without a shred of evidence.

edit: to make clearer the Anglo-Saxon references; the Old English word is a cognate (related to) the Romance language word that eventually gave English the word "ogre" - but that importation followed a different route and was not part of the English language during the Anglo-Saxon period.