This is the trick I use with old clothing ....
In a large bucket, mix equal parts Biz (yes,the brand name) laundry detergent and Dawn dishing washing soap (original blue formula) in hot water and then soak the article for a couple of days. I use about 0.25 to 0.5 cup of each product. Wash/dry the article as desired.
This has worked about 80%+ of the time on the first try. If I see improvement, but still traces of the offending spot I will go for a second go around.
The real hard part of this treatment is the time. The more time you allow the item to soak, the better chance of success.
Good luck on removing the offending spots.