Polyester, an inexpensive, durable fabric made of synthesized polymers, will last for years with proper care. Like any fabric, polyester can stain if exposed to certain elements, like oil. Removing dried oil from polyester poses some difficulty, but you can do it with some common household products.
Lay a white towel on a flat surface. Place the polyester fabric on top of the white towel with the dried oil stain facing up.
Dampen the dried oil with cool water.
Rub a pre-wash stain treatment into the dried oil stain. Allow the pre-wash stain treatment to soak into the stain for 15 minutes. Alternatively, use a grease-cutting liquid dish soap in place of the pre-wash stain treatment.
Launder the polyester as normal. If the dried oil stain remains visible after the wash, do not place the item in the dryer. Instead, repeat Steps 1 through 3 until the stain disappears.