Authority is meaningless unless others know that you possess it. It became quite important to display these bones to the public. The collections grew apace with the passion for collecting bones of the "heroes." Not only bones, but such objects as Medusa's hair, pickled mermen, and the egg Leda laid after her encounter with Zeus which occurred after he had been turned into a swan!
Gryphon claws and eggs were in these collections too and some were still on display in the Middle Ages. That these completely misunderstood bones should have held such importance to the ancient Greeks and Romans shouldn't probably be much of a surprise.
In much later years the Habsburg dynasty and their remains were treated rather "specially" too. In 1618 the church of the Capuchins in Vienna, a 'new' order renowned for an asceticism and evangelizing fervor, was selected as the last resting-place for the bodies of the Habsburgs. However, their viscera and hearts were placed in silver caskets, rather like the Canopic jars of the Pharaohs, and presented to the church of the Augustinian order, where they were kept like Phillip II's relics, in rows behind the high altar. The entrails, the seat of the emotions, were the right of the Cathedral of St. Stephen's, where they were received with due reverence in their silver caskets. There is something in human nature which makes people want to venerate the bones (and other body parts) of mythical (or imaginal) creatures, religious saints and royalty.
Not everyone believed in the truth of what these bones were said to represent. The more orthodox scholars, such as Thucydides and Aristotle, seem to have ignored the subject completely. They-like other men of learning were already sure that the myths associated with such difficult to clarify bones (and the supposed creatures who left them) were false. Others were not so sure. We know now, of course, that the bones were not those of actual gryphons. However, could they have existed on another level of reality alongside us? Daimonic creatures seem to exist along some sort of spectrum, some appearing at the personal level; others at the impersonal level.
From Patrick Harpur's Daimonic Reality: A Field Guide to the Otherworld: "The most stiking of these apparitions come in animal form, notable bird-like creatures, black dogs and cats, lake monsters, and "big hairy monsters...Already these suggest an affinity with a certain element or type of landscape as the Neoplatonists noticed. Olympiodorus, for example, remarked that daimons can be celestial, ethereal, aerial, or subterranean. (He adds, for the benefit of ufologists, that "irrational daimons originate from the aerial governors...") My emphasis added.
I should have about one or two more articles to go for the "gryphon" part of this series. After that, I would like to keep going with looking at other mythical (or not so mythical) creatures and some other things in between. Thanks for your intelligent and thoughtful comments! All the best to anyone stopping by!