Get rid of stain

Unfortunately, stains on paper that are already attached to book board cannot be removed by chemical means. You could use some gentle dry methods such as erasing but if the stain is set into the fibers this will not work. Sometimes, you can ameliorate the stain with careful scraping on the darkest parts to make it blend in more. Applying any chemical or even just water will further damage the area creating even worse staining is a different way. Anything you apply will not be washed out and so it will continue to affect the paper.

If you are truly desperate to remove the stain, you could remove the entire cover and wash it and then replace it. As you might imagine, this is not for the faint of heart.