We seem to have developed a slow water leak at the bottom right edge of the casing for the water dispenser in the left door of our GE refrigerator. This is causing water to drip slowly along the front face of the door all the way down to the floor. The dripping water is stagnating on the wooden floor causing the wood to slowly warp. Here are some pictures showing this.
How can I stop this leak?
-- update --
The leak seems to be because of water under the drip tray, but this water is not overflowing -- there has always been a small amount of water stagnating under the tray for the last 4 years without this leakage.
Including picture of model number.