Fingers can't get sick

My 3 year old gets a cut on her finger and I put a bandage on it. Later on that day as we are in the car riding to the store she tells me that her finger feels better and wants to take the bandage off. I explain to her that she has an open cut on her finger so to keep her bandage on. She says huh. I attempt to explain in preschool terms and it goes:

Me: I want you to keep your bandage on so your finger doesn't get sick.

J: What?!? My finger can't get sick, it doesn't have a mouth.

Me: But germs can enter through your cut and make your finger sick.

J: Huh?!? That doesn't make any sense.

I still haven't figured out how to explain to a 3 year old how a bandage protects cuts from getting infected.

Luckily this one didn't get "sick" :)