Doctors of old prescribed Lugol's for their patients and had them paint the soles of their feet before retiring for bed. They were to "repaint" ONLY if there was no more stain. I've done this with povidone and got some VERY softened callouses out of the deal; it made fast work of the pumice stone in the shower.
Povidone is not Lugol's but IS the strong Iodine diluted by today's doctors to make "betadine" used in treating open wounds. I know, because that is what our home-care nurses used on my husband's foot post-surgery to save it from amputation.
I use the povidone I still have left on any skin issue - burns, bruises, the breaking of toes that can't be given splints, the stuff's remarkable.
So no, don't throw it away
Just be VERY careful around the face
and know that it stains!