J.S.
Sometimes I find these "grease stains" on our clothes too. It's really bizarre. My husband had a brand new t-shirt that he only wore once or twice and when I pulled it out of the dryer, those stains were everywhere. He's not a sloppy person so I have no idea how they got there. Several years ago my dad turned me on to this product called Carbona. It is small yellow bottles of stain remover. They have a different bottle for different stains. I've used the grease/oil bottle and have successfully gotten these grease stains out of our clothes. You can't find Carbona everywhere though. We have several Walmart's in our area, some carry it in the laundry aisle, some do not. I think you can also buy it at JoAnn's Fabrics. I swear by Carbona now. I have many bottles for all types of stains in my laundry room.
Here's a website so you know what they look like.
http://www.carbona.com/stain-devils/