This has bothered me for years.
Just now finished trying the following (and it WORKED like a miracle!!!!!):
Hydrogen peroxide on the brown stain and rubbed it vigorously between my fingers.
an OXI stain remover (I used Preen I bought in Australia - but others have the Dual Action with Oxi Cleaner)
- rub it vigorously.
Bleach which was safe for Dacron,
synthetic fibers - and rubbed it vigorously.
Rinsed in cold water - rubbed and squeezed.
First time EVER!!!
This was on a white cotton OLD knit top.