Removing permanent marker from china dishes requires the right kind of product: the same products you would use for removing marker from other porcelain ceramic items such as tiles. You can't remove permanent marker once it has dried with soap and water alone, nor will bleach products affect it much. Straight bleach may fade the stain slightly but won't dissolve it. You must use solvents to remove permanent marker from china dishes. You don't have to use paint thinner or acetone, although either will usually work. You can instead remove marker using less toxic solvents that you may already have around the house.
Spray the china dishes with WD-40 or spread rubbing alcohol over the marker stain, using a cotton swab or ball. Wait one minute before continuing.
Wipe the marked area of the dishes with a dry, soft cloth. Much of the marker should be transferred to the cloth. Try to wipe only the stained areas -- don't spread the ink around. Apply the WD-40 or alcohol again.
Use a clean cloth to remove more of the marker stain. Apply more WD-40 or alcohol if necessary and rub the alcohol or WD-40 over remaining stains until all the marker is gone.
Wash the china dishes in dish soap and water to remove traces of alcohol or WD-40. Rinse the dishes well and dry them with soft towels.