How can I replace the rear display housing, part number 922-7898?

No it is probably not covered by Apple Care.

It's not easy at all. First you'd need to find a replacement one, which probably means buying an entire display assembly, then you'd need to take of the glass by melting the glue all around it with a heat gun, which is risky, you could damage the rubber or the lcd itself.

if you want to make your own opinion, here is the guide for a unibody macbook : MacBook Unibody Model A1278 LCD Panel Replacement