In you scenario, no, the light would not bounce back. I think the problem in your thinking is that light expanding does not count as an expanding universe, but really it should. Even if this were not so, the light needs something to reflect off, but it can't bounce off nothing.
"In physics, radiation describes any process in which energy travels through a medium or through space."
There is ionizing, and electromagnetic radiation.
All electromagnetic and light waves, including microwaves, sunlight and radio all travel at the speed of light. 186,000 miles per second.
Electromagnetic includes light, and so they could just measure the light. In this case they are measuring microwave radiation which thus seems plausible since it travels at light speed.
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