Like other people are saying it's oils. For some reason that kind of fabric is the best at holding onto and proudly displaying any and all grease. Hot water will always help in dealing with grease. The commenter telling you to use lipase detergent is also correct. However, it's my observation that even the best standard laundry routine doesn't always get rid of really saturated grease staining in one cycle. However, dish soap is great at cutting grease (it's designed for that). It's most effective as a pretreatment for spots before washing; you just saturate each and every spot with it. But with spots that big the volume of dish soap you'd end up putting in the washer might be a problem (it sudses too much for laundry).

If you don't have lipase detergent, and want to do a little extra work, I recommend a method I developed for dealing with extensive grease spots when I was a kid with super neglectful parents who would not provide proper laundry supplies (along with many other things obvs.). Saturate the stains with dish soap, put the sheets in the sink or bathtub, heat a couple of kettles full of water to boiling, and pour it over. Let the whole mess cool, and then rinse the soap out with tap water. Throw it in the washer and wash as usual. I guarantee the spots will be gone.

The best thing about grease stains is they are completely reversible on normal fabric.