I also scatter feed for the same reason. I think the mice pee in the bowls constantly...like they've confused it with the potty corner and then it's very unhealthy and I have pee crusted oats to the bottoms to try and soak off. I notice when I dump the food the mice enjoy looking for it and making tunnels out of the bedding while doing so.
My meeces do the same things. I use milk and water bottle caps for feeding prgnant and nursing does, and they like to try to incorporate the lids into the nest about half the time. With bigger dishes, they empty out the food and climb into them, turn them upside down, fill them with all kinds of litter and etc....I guess it gives them something to do.
ahh yes, I've just checked their bowl and there's wee in it, how lovely! For now i have just cleaned & disinfected it and put more food in, when i clean them out i will start putting the food on the bedding