A: They put the new carpet down on top of the old carpet, in the same way that they painted over the wallpaper.
B: They bought special inflatable carpet.
C: They bought special organic carpet consisting of a layer of fabric laid over a stagnant bed of wet spongy bog peat.
A seems the most likely answer, stupid as it is. B would also be acceptable. Unfortunately it's C that keeps popping into my head whenever i'm walking on it =P