Wet an old toothbrush, nail brush or nylon scrubbie with lemon juice, dip it in salt and scrub the mildew area. Rinse well with plain water and dry.
Dip the brush or nylon scrubbie in bleach and scrub the area. Scrub not only the mildew area, but all of the grout because the bleach may lighten the color of the grout even if it is white.
You don't want obvious white or lightened areas of grout. Rinse the area well with plain water and dry.
When working with bleach be sure to ventilate the area well and wear eye protection and rubber gloves.
Allow the grout to dry overnight if the mildew stains remain after you have tried other cleaning methods. Paint over the mildew stain with grout paint or a white correction fluid.
Allow it to dry then seal your grout with a grout sealer to prevent future staining. Grout paints and sealers are available at hardware stores and home improvement stores.