I have a 2002 Sequoia.

When I put the car into reverse and pull out of my driveway downhill while gently applying the brakes, I always hear a gentle screeching sound.

Any ideas why this is happening? I have plenty of pad thickness left on the brake pads.

 

Is the dust shield bent or a rock or pebble wedged? It could be rubbing. Did you replace the pads and not have the rotors resurfaced? Sometimes the directional lines on worn rotors are like a vinyl record with new pads and they squeak.