My daughter bought the 5C in October 2013. In November, we made an appointment at the local Genius Bar to ask about the screen popping (sounds like the home button) when you press on various parts of the screen.
Person at the Apple Store replaced the phone saying they agreed it didn't seem right that the screen should make that popping noise, though the screen was still solid within the plastic case.
The new 5C eventually started doing the same thing...so we returned to the Apple Store in late December. This time, they said the popping sound was a "design feature". They claim the Apple engineers designed the screen to "give" to make the phone more durable. They said they were not told of the "design feature" until they had replaced a bunch of 5Cs.
I explained that my fear was that the "design feature" would eventually result in a flaw with the 5C after the warranty expired. They said that the 5C just won some award and I should not worry (like those awards mean anything). They also suggested I purchase Apple Care in case there was a problem after the warranty. Of course, I pointed out that the 5C just won an award and I shouldn't need Apple Care.
The 5C screen seems to pop more when it gets hot from use. To this point, it does not affect the function of the iPhone, other than to annoy my daughter when it's doing it a lot.
I've seen many reports on various websites of this issue, so thought I would share what Apple is now saying (at least at my local store in St.Louis).