At least get rid of the stuff that is leaking out now !!!
Buy some "cleaning vinegar" or I think its called white vinegar and rinse the battery area where the stuff is with it.
Make a video, its fun to see the bubbles !!!! After the bubbles are all gone, the stuff left is chalk. You can scrape it away pretty easily.
Dont get the entire board wet. At least that battery is nicely positioned in the corner. Store the PCB so that the battery is on the BOTTOM, so that if there is any leaking, it will run away from the electronics and not towards it.
Does the PCB actually work by the way ? The label of the closest EPROM seems to have become wet at one point in time.....how about the chips around it ?