Do you hear the same noise when you are accelerating? I would be surprised if it is your diff if only on braking.
A few things to try
1 - Check that your motor screws are tight and that the motor isn't moving when you brake.
2 - Take the pinion gear off and make sure the drivetrain moves freely in both directions
3 - If this is a brushed motor do a test with the pinion gear off on the workbench ad see if the motor is making the sound.