I think Randi missed the problem, IF i understand the OP. I understand it to say the the two fans on the CPU cooler (push / pull arrangement) both move air from the BACK of the case towards the front. Thus they would complete with any rear exhaust fan for air flow in the same immediate area. Not a good arrangement. I presume (is this right, OP?) that the two front fans are intakes, and the two on top are exhausting out of the top.
My preference would be to keep the rear fan in place, but ONLY if you can reverse the mounting of the two CPU cooler fans so that they blow air through the heatsink in the opposite direction - from front to back of the case. That would require removing them, turning each fan around and re-attaching each to the heatsink. Usually that's not a tough job. BUT it also means that there must be good air flow from the area in FRONT of the CPU cooler system (between its fan and the case front) so that the re-oriented fans do have a good source of cool air to use. IF that area has good air source AND you can re-orient both those CPU cooler fans, you could do this. Otherwise, I agree that disconnecting and removing the rear fan is correct.