I don’t follow archeology directly, but every couple months I listen to the Unearthed! episodes of Stuff You Missed in History class, which goes over the prior quarter’s archeological news. A whole section is dedicated to reciprocations, because there are tons of complaints. UK museums still refusing to send back stuff stolen from other lands, items found to have been illegally taken, etc.

So it’s more if nobody the people who run the place cares about complains.