They replace it with the equivalent model.
Not always true. My friend bought a refurbished 1st gen a few weeks ago and the wifi didn't work. He sent it back to Apple, and instead they sent him a brand new 2nd gen. I'm guessing it was an exception.
But, in the OPs case, I'm not even sure they will replace it. They might just clear out the dust from under the screen.
It's a simple process to take the screen out. And no do not even think about trying it because you need the right tools.
Apple will replace the screen for you. This is not garunteed because I have heard my cousin, he works at the store, tell me that they become lazy so sometimes they change the whole product and throw this out. Don't rely on that, i think it's false.
Anyhow, they will most likely pop the screen out and change it.