Put on rubber gloves and a dust mask. Open the porcelain tub room's windows to ventilate the space because you may spend a significant amount of time cleaning the stains.
Pour denatured alcohol onto a scrub sponge, and use the sponge to scrub vigorously over the magic marker stains on the porcelain tub. Scrub until the magic marker stains are gone.
Wet the porcelain tub using damp paper towels to remove the denatured alcohol. Wipe the tub with dry paper towels.