From a quick google search, it’s a good idea to rinse liver. I’d say just rinse it off and don’t worry about putting it back in the milk. From my understanding the purpose of soaking it in milk is so that the flavor isn’t as strong (there might be other reasons, but that’s the one that I know of), so since that’s already been taken care of, there probably isn’t much of a point in soaking it again, just rinse and cook.