Since both cork and flax are natural products, the cases aren't completely flat. This means that dirt and discolouration can show of more than on a regular plastic case since it gets stuck in-between the fibrers.
You can use isopropyl alcohol to remove stubborn stains, or take a sponge with dish soap water and rub the case with it.
Note that the printing on the cork cases is not black color. It's laser print, which means that the black actually is burnt cork; it can transfer to the rest of the case after a while.
Over all, try to avoid dark jeans and food, those are the stains that are the hardest to remove!