2016 fit ex-l, ~60k miles

When i start up the car and go in reverse (when I actually start moving in reverse), I get this weird whine. Information on the whine:

-It's only when I am actually moving in reverse.
-It sounds like a dry, squeaky pump that starts and stops - it's not a continuous whine.
-The whine stops when I hit the brakes while in reverse, and then continues when I let off the brakes.
-If I don't hit the brakes and continue in reverse, it eventually stops after a few "pumps". However, it happens every time I go in reverse, not just once. So if I go back into drive, and then back into reverse, I hear the same whiny pumping
-It sounds like it's coming from the front of the car. I have no idea what it could be, and there are no indicator lights on.

I'm at about 60k miles, and I just flushed my coolant (this noise was here before I flushed the coolant). Any idea what this could be? I'm going to check the rest of my fluids this weekend.

thanks

 

Best guess? Transmission fluid line is clogged or needs a new filter. The noise you hear is the fluid trying to get through the obstruction.