Vintage quilts need to be handled with care. Although you usually would avoid exposing an old textile to direct sunlight, sunshine is the best way to kill mildew without damaging delicate fibers. Leaving your quilt outside long enough to kill the mildew won't damage the fabric, but ignoring the mildew will. Once you have removed the mildew, let the quilt dry completely before storing or displaying. Store the quilt in a dark, dry cabinet, or display away from moisture and direct sunlight to protect it from mildew and other damage.
Spread the quilt on a tabletop or large work surface. Look at the quilt surface and identify the areas that have mildew.
Fill the plastic cup with warm water. Dip the toothbrush in the cup and then into the baking soda. Use enough baking soda to coat the brush bristles completely.
Gently brush each mildew spot with wet baking soda. The soda will combine with the water to form a paste that is of toothpaste consistency. Dip the toothbrush in the warm water and baking soda as needed for each spot.
Use the cap from the vinegar to pour a capful of vinegar on top of each of the treated spots. The vinegar and baking soda will bubble; this is a chemical reaction and is normal.
Blot the mildew spot with a clean towel to absorb the excess vinegar mixture.
Fill the sink with warm water and add 1 cup of lemon juice. Immerse the quilt in the sink. Soak for 10 minutes.
Drain the sink. Squeeze the water from the quilt by gently pressing the quilt against the side of the sink. Do not wring the quilt.
Hang the quilt to dry outside in direct sunlight. Remove promptly when dry. if your quilt is extremely fragile, don't hang it, just spread it out on top of a clean blanket on the lawn.