It is usually complicated to remove rust stains from fabrics, especially delicate ones that cannot rub a long time and on which you prefer not to use bleach or other products, with the fear that they are a little aggressive. Often it gives up, thinking that the only solution is to throw away the head, now useless. Instead, try to follow this system.
As I said, rust stains are difficult to remove, and to do that, it takes a bit of time and patience. But have faith that even those impossible stains can be defeated using simple ingredients usually found in every home: table salt and lemon juice.
Proceed as you pointed to wet tissue in the area where the stain is located using very little water; It covers the whole area with the fine salt and wet with plenty of lemon juice.
Put the sun to dry. Now check if the stain is gone. If it’s gone, then proceed to wash the garment normally, even to remove the slight halo that may have left the lemon juice.
In the case, verifying that the stain is still present, although maybe very attenuated, repeat the process until they can no longer see any sign of rust. I applied this method on cotton fabrics and mixed (synthetic/cotton), always with success. I’ve never experienced silk, then this type of fabric cannot guarantee success.