I have been told that shampoo will remove oil. I'm not sure if it works, but the theory is that shampoo is made to remove hair oil so should remove it. I think I would try the Dawn since they use it to remove oil from the birds that get trapped in the oil spills in the ocean, so it should work for this. I would be hesitant with peroxide since it is a bleaching agent and could remove the color from the quilt. Let us know what works for you.
Sue