I'd imagine a c-band micowave receiver was a receiver used in a microwave link in the c-band. I believe most of them now have converted to other frequencies or gone to fiber links because you don't hear about microwave interference as much as one used to back in the 1980's.
today's big c-band interferer is homeland security/military.
It could be a C-band receiver that accepts a direct LNA feed. There were at least commercial receivers that worked that way, and at least very early home TVRO receivers.
Then there is terrestrial microwave, which is usually in the 2 Ghz range.
Microwave is generally point-to-point, and by now all digital, using custom modulation.
There were, or still may be microwave pay TV services, that began as analog using essentially a modified analog cable box, and went to more or less a satellite receiver with a demodulator made for that format.