Greek art was influenced by the Near East in their early period, the Minoans and Mycenaeans shared art through trade, and the Egyptian artists were influenced by whoever invaded their culture. The Greeks exported a lot of pots to surrounding nations such as the Etruscans in Italy, so we’ve found a great deal of Greek pottery buried far outside Greece. The Romans loved Greek art, so reproduced it in marble. It’s hard to answer the question of who owns what, if the basis is ancestry or location. If the art belongs to the nation that lives on the land now, it’s not very fair to the nation they displaced. There doesn’t seem to be an easy answer, so what may be fairest (but potentially unpopular) is to agree that art belongs to human kind.
The image of the Gorgon may have been adopted by the Greeks from the Phoenicians, and may have taken the image of Aphrodite and her associated symbols as well. Ancient peoples shared and borrowed art and ideas just like modern people do. Ganguro girls in Japan make themselves up to look like Californian Barbies, while shy boys in American high schools adopt Japanese dress and behavior from watching anime.
It seems to me that if we all came from walking apes in Africa, and are naturally inclined to share and mimic art and ideas, then art belongs to everyone — including ancient artifacts. We should be working on making it easier to share, and make it easier for the descendants of the ancient artisans to visit their art — or help them create museum spaces to keep the art close to home and generate revenue. It is also more possible to create reproductions of art, due to 3d scanning and printing, so it should become easier to share the experience globally.
I think we should think more about what the original artists would feel — such as joy that their work is still being enjoyed thousands of years later — and act less like children fighting over their grandfather’s will.