Can I repair a pan where a spot on the bottom changed after staying too long on the burner?
From the way that picture looks, this is a sandwich-bottom pan with some thin kind of coating on the bottom. That coating seems to have come off. In that case, there is nothing you can do to make it look the way it did before. 

If I were you, I would just continue to use the pan as-is. No need to throw it away, as it will still work, and no need to try to change something about the spot, as it is not really repairable. 

You'll have to test how reactive the new surface is. If the now-visible layer is aluminium or blue steel, it won't do well in a dishwasher. If you see the spot rusting (or getting some other kind of corrosion), clean away whatever has built up, and from then on, only wash the pan by hand.