Soaking might not be enough to get all the starch out. The seams might require some gentle rubbing with a soapy finger.
If you do decide to overdye, it's best not to use tea. Tea contains tannic acid, which shortens the life of the fibers. Any type of light tan fabric dye would be better. Or, I would look for some white fabric paint to touch up small areas.
I am most likely to scorch starch by using spray starch and not giving it enough time to dry before hitting it with a hot iron. It does help to spray one side, turn the block over, and iron the opposite side. It's best, however, to wait long enough for the fibers to absorb the starch completely before ironing.