Did the Plate Umpire look at his hand before he got back to the dugout after the Top of the First? I was watching the ESPN stories, and it looked like the conversation between Rogers and the Umpire took place during the Second Inning, after the hand had already been washed.
I may be off base here, but that is certainly the impression I got.
In any case, unless LaRussa requests an inspection, there is nothing to inspect. If there was any failure here, it can be placed at the feet of LaRussa.
From the article : "after the first inning, Alfonso Marquez, the home-plate umpire, asked him to remove the dirt so there wouldn't be any question about any controversy."