Ok, before anyone jumps in and says to check your grounds or any other such nonsense you need to see where the problem is exactly. Wife your front speakers are fine it's probably not the amp but we're going to make sure.
First, swap front and rear RCAs. If the noise moves to the front it's the rcas or the integration adapter. If it doesn't, swap the RCAs back. And swap the front and rear speaker cables. If the noise moves it's either the amp, rear speakers, or rear speaker wires. To find out which, connect a known good speaker and see if there is noise. No noise means speaker or wire. Noise means bad amp. If there's noise with the test speaker run a new speaker wire to one rear at a time and see which makes noise. If nothing on either, it's the wire. If only on speaker, replace that speaker.