There are various possible causes for grease marks on clothes after washing. To try and prevent it always make sure you use a good quality detergent and use the correct amount. Don’t overload the washing machine either.
Not using enough detergent combined with overloading can cause poor wash results and redistribution of grease onto laundry. So something that didn’t have grease spots on it before can come out of the wash with one on.
How to remove grease marks or spots on clothes
Oil and grease spills during meals or during cooking can be particularly stubborn to remove from polyester. Pre-treat with something like Ariel Liquid and wash at the highest temperature recommended on the care label of the article.
Try using washing up liquid and an old toothbrush. Put some washing up liquid onto the toothbrush and gently rub the affected area round and round with it. After treating, put the laundry back in the wash on the wash cycle recommended for the garment as stated on its wash label.