Starbrite is my "go to" product for non-skid but different stains require different products.
You call this a "stain" but it's possible it's part of the carpet backing. I would try acetone. Let it sit for a minute or two and scrub and see if it has any effect. Acetone is a solvent and will dissolve the bond if it's part of the carpet backing.
It's best not to leave acetone on the surface for longer than necessary so regardless of if it works or not, use soap and water to remove it and rinse well.
Mr. Clean Magic Erasers (grocery store or home center) are a very mild abrasive and work well on vinyl upholstery and may help on your non-skid if nothing else works.
You could also try commercial "hull cleaner" (acid based) on the stain, following the directions on the product. Again, rinse thoroughly.
Sometimes, long term exposure to sunlight makes a stain go away on its own. I'm talking a few weeks.