Diagnosis
You need to run a cleaning solution through the entire internal water system, not just wipe it down.
How to Fix It
Power off the machine. Fill the water reservoir with a mix of 2 cups white vinegar and 2 cups water. Turn the machine on and press the 'Clean' button (if your model has one) or simply run a full ice-making cycle, letting the vinegar mix cycle through. Dump the first batch of ice. Then run 2-3 cycles with clean water to flush.
If That Didn't Work
For heavy scale, you may need a commercial descaling liquid made for coffee makers/ice makers. Follow the product's instructions.
Heads Up
Never use harsh chemicals or abrasives. Vinegar is safe and effective for regular maintenance.