Ford fiesta 2003 reverse gear sound...

most car make a whiring sound in reverse because the reverse gear is a straight cut gear as opposed to helical cut. straight cut gears are noisey.

I just thought of something is the car moving when you put it into reverse? reverse gears don't have syncros so they will grind if the car is not fully stopped.

nothing should be wrong with your transmission.

if you are only having the issue in reverse that would make me lean more towards the transmission having an issue than the clutch.