Hunter sent me a replacement receiver - but I can't seem to figure out how to remove the old one from the ceiling fan. Any help?

Be sure power is off. It should be inside the canopy at the ceiling.
Look here:
Hunter Ceiling Fan Remote Control / Receiver NEW | eBay
Red and white on the receiver shown has a red and white that needs constant power, some are black and white. Then the 3 wires out go to the fan connections, white is neutral, black for fan, and blue for light.
They sometimes can be tough to remove or install in canopy.