It'd probably stick pretty easily if they put the things back in the Parthenon, they're only know as the Elgin Marbles as the Earl of Elgin looted them.
As a simple example, the Rosetta Stone that is the focus of this article was yoinked by locals for building material and used as fill in the wall of a fort some distance away from its original location. It was only saved because when some French soldiers were rebuilding the foundations of the fort wall someone recognized the significance of the inscription on the stone.
It is a sad fact that were it not for this 'looting' we would have far fewer artifacts to examine and use to inform our understanding of the past because the locals would have continued to treat these sites and objects as open-air quarries.
And I would accept this excuse if they now returned the items they looted to the countries that do have significant preservation efforts in place. Like Greece.
Sure the British could have been worse, but they were still pretty bad.
many idols of gods in less famous and out of the way hindu temples in india were stolen and sold off to collectors in the west. these idols were there in the community forever and cared for, when they were stolen, the community simply accepted the loss because they didnt have the resources to chase it all up.
see this: https://www.newyorker.com/magazine/2007/05/07/the-idol-thief
from the article
Collectors often suggest that they are the custodians and preservers of antiquities that might otherwise suffer from neglect or mistreatment, but Ghiya described the callous mechanics that are sometimes required to smuggle a statue from one country to another. He recalled a squat stone Vahara—a depiction of Vishnu in his incarnation as a boar—that stood in the village of Attru, in southeast Rajasthan. The boar weighed more than a thousand pounds and its legs and torso were covered in a magnificent phalanx of tiny, intricately carved figurines. Ghiya’s thieves stole the statue in the late nineteen-eighties, lacing a chain through the boar’s open mouth and yanking it from its stone pedestal, shearing off its lower jaw and breaking its legs in the process. The piece was eventually sold to a private collector in Zurich.