I just realized the button battery in thermometer i've been using rectally on my toddler corroded. there was acid all inside. will this hurt my child?

Battery: The corroded button battery can cause a great deal of trouble if swallowed if not washed off immediately the acid can cause skin burns.

Amount outside ?: Any leakage that was contained within the battery compartment and not reaching the probe surface should not be a problem.Such material might cause a surface burn on any skin touched if it was on the surface of the probe and used.