Sincé the stainless Steel should be resistent to álcalis, you can try soaking with a 5 to 10 % solution of KOH in etanol. Time of treatment between 2 to 6 hours with same refreshing of the alcaline coating.
After treathment, wash with plenty etanol, wáter a 5 % solution acetic acid and finally plenty destiled wáter. Good luck!