Alas, I managed to stain one of my books as it was sitting close to me while I was eating. I hate this when it happens (it has happened once or twice in the past), and I tried to find a way to clean the book.
Lifetips.com has this useful tip:
Tip: Removing Oily Stains
It is possible to remove most oily or greasy stains from book pages. You will need some paper towels, a dry cleaning pad (available at drafting supply stores and most stationers) and a soft-bristled brush. First, place paper towels between the affected pages. Close the book and weight it with another book of similar size, then leave it alone for a few hours. Discard the paper towels and examine the pages. If there are still some stains, take the dry-cleaning pad and twist and squeeze it (or even cut a corner) to sprinkle the powder inside onto the stain. Cover the stain as completely as possible and leave the book lying open for a few hours. Brush the powder away with a soft brush. For very stubborn stains, rub the powder in VERY gently with a gauze pad, and let sit overnight. Residual powder can be removed with a small hand vac. Vacuum from gutter to edge.
I’m not sure this method works, but it’s worth a try. For more tips on books, get this PDF.