Rust should be cleaned using the Water Based Stains Cleaning Method. This type of stain can be removed with excellent success by a professional.
Tools & Technique:
Using a neutral pH low residue spotter, apply a small amount to cover the stain , blot and repeat blotting until the stain is removed. The idea here is to transfer the stain to the terry towel by applying the spotting agent and removing the stain by blotting with a dry terry towel.
An alternative spotting chemical is to mix 1 tsp. of neutral pH liquid detergent (dish washing or fine fabric detergent that does not contain any bleach ) into 1 cup of warm water. Tamp, do not scrub as this may distort the texture of of the pile. Cover with a white terry towel and press down repeatedly blotting up the stain as described earlier.
If the spot or stain turns brownish when dry, mix 1:2 white vinegar and water. Apply a small amount and blot. Repeat only once.