Shiny iron stains on polyester are caused by a hot soleplate melting the fabric. For this reason, it can be impossible to remove these shiny stains. However, we do have a method you can try.
Dampen a white cloth with 3 percent hydrogen peroxide or a scorch removal product.
Test in an inconspicuous area of the garment like inside the shoulder or under the hem.
Gently rub the shiny stain with your dampened cloth.
Launder as normal.
Repeat if necessary.
If the stain cannot be removed, unfortunately, it might be permanent.