Diagnosis
That’s the ice maker’s fill valve clicking on and off. On this model, the water valve is mounted on the back wall of the fridge compartment, so the sound transmits right into the kitchen. It’s normal operation, but annoyingly loud.
How to Fix It
You can’t stop it from clicking, but you can muffle it. Pull the fridge out and check the water line connection at the back. Make sure the plastic water line isn’t touching the fridge’s back panel. If it is, put a small piece of foam or a rubber grommet (even a folded cloth works) between the line and the panel to dampen the vibration.
If That Didn't Work
If the clicking is constant or rapid-fire, not every few minutes, the valve might be failing. The part number is WR49X10055 (the water inlet valve). It’s a DIY replacement if you’re comfortable shutting off the water and disconnecting the lines.
Heads Up
Don’t try to oil or lubricate the valve. It’s a solenoid-operated part, and any foreign material can ruin it or contaminate your water line.