Thanks for the closeup of the battery, but if you look at the area where the "green" covering meets the metal, you will see a white powder; now either your battery is snorting cocaine, or you see the white salt of corrosion.
My vote is for the latter. Please note that that battery is a 3.6V and the coin cells are 3V; added to that the diode removes about 0.3 to 0.4 volts and if you want your clock keeping time, you should get a new 3.6V (unlikely to leak) battery (from AmigaKit). Removing it is simple if you don't plan to replace it, just clip the three legs.