What is the "loaded resistor" for ultrasonic receivers?
I guess they mean load resistor, not loaded resistor.

A load resistor is like a dummy. You can use it to test a power supply, antenna tuner, .... Instead of the device you'd connect normally to the device you want to test, you connect a dummy load or load resistor to it, so that if something goes wrong, you mess up the dummy and not the real device.

About your datasheet: the manufacturer did some tests with his device and a dummy load or load resistor. The diagrams give explanation on that.