There has been an issue that British Museum had looted treasures during colonial period. While some countries nowadays are angry and claim they want British Museum to return to where they were initially belonging to.
In my opinion, now is an era of global village that human being can easily gain information from internet. Nevertheless, people are still more interested in paying for anything kinds of transportations fee to get to the museums or galleries just to get to look at the authentic piece in person. You might not be charged when you go to Chinese Ceramics Collection in British museum which is great but it does rich the cultural aspects of UK while they supposed to stay in China. Besides, it does affect to the aspect of tourism as well.
As a result, I will say it should be returned to where it is originated from unless the two countries negotiate well whether purchasing from the originals or other sorts of diplomatic methods.