The char itself can also be conductive - the carbonization of the resin binding the fiberglass effectively becomes a resistor. Fraser has the right approach, though, you physically remove the charred PCB material and then jump over wires for the traces you removed - at least in small areas and without too many board layers this method works well and can be done with a dremel and some patience.
Worth mentioning that if you've got a leaky battery, very often the battery chemistry means the leaked fluid is actually alkaline in nature, so while neutralizing it is a good idea, you would normally do a cleaning pass, a mild acid to neutralize the residue and stop the erosion of traces, and then another rinse or two to get rid of as much as possible. It should be easy to determine the kind of leak it is, you can take a drop of vinegar or a drop of baking soda water (or similar base solution) on the leaked fluid and see if it bubbles. Just be sure to remove the drop completely unless you are intending to do all the cleanup of it then, as leaving the reacting chemical in place can do more damage if left there.