The carillon at the International Plaza wasn't the only one at the 1964-1965 New York World's Fair. In fact, there were two others. This was the largest one, located in the Belgian Village. It was visible from much of the fair grounds and for a good distance outside. The tower was built quite sturdily, and after the fair it was used in an engineering study to test building designs for earthquake safety.
The bells weren't inside during the earthquake testing, and if they were I imagine they would have made a dreadful racket. The engineers doing the testing didn't have to worry about removing the bells first, though, for someone did that for them. The night the fair closed someone cut the bells free and dropped them to the ground, carting them away to never be seen again.