Gently and patiently twist one tile at a time until you get them to come loose, starting with a tile where the string came loose. You should be able to get them free without really knowing what you're doing, if you do this a while. It shouldn't require a lot of force, just twisting in various directions until they come loose.
After a couple of restringing attempts, you will eventually get where you can restring without taking it apart. But for a first try, I think it makes sense to take the whole thing apart. That way you'll understand how it's put together better.