The UK has long refused to return the contested sculptures, which were stripped from the Parthenon in the 1800s.
The daylong demonstration culminated in a mass action and occupation of the museum after hours.
The protesters also targeted the British government’s controversial plan to build a road near the Stonehenge site.
The Institute for Digital Archaeology hoped to scan the marbles and create an exact replica that might help settle the dispute between the London museum and Greece.
The disgraced family’s name will remain on the museum’s benefactors’ board and its Great Court donor list.
The institution’s announcement follows a protest at the British Museum this weekend over oil giant BP’s sponsorship of its Stonehenge exhibition.
But the discovery was drowned out by the drumbeat of protest against the British Museum following new revelations about its ties to a fossil fuel company.
Users can view pictures of objects set against backdrops illustrating, for instance, the sacred rites that they once presided over, but also violent occupations and sieges that unrooted them from their communities.
The principle that one misdeed deserves to be redressed before another, because it stems from a situation of greater violence, is wrong.
In a meeting in London, the Greek Prime Minister reiterated an offer to loan other artworks to the British institution in exchange for the priceless marbles.
To do so before they have returned the Maqdala treasures and the Benin Bronzes and the Easter Island statues and the Maori heads, before a coherent set of precepts for decolonization has been articulated, would affirm the wrong principle.
“Everybody in Mesopotamia, as far as I understand it, believed in ghosts,” said Irving Finkel, a curator of the British Museum’s Middle Eastern department.