I found it's a fungus, as mis-recognized as the cancer fungus apparently. And fungus are notorious for their difficulty to get rid of.
Hum, an idea, If you rub olive oil on it, does it help some? Or help completely, because olive leaf and olive oil are anti-fungal. If it does help a bit, then invest in some silver gel to get rid of it quicker. I never did that, since I had the gel on hand, but it should at least give some indication, one way or the other.