Diagnosis
You can, but it's the fastest way to degrade the non-stick coating. The harsh detergent and high-heat drying cycle in dishwashers will cause it to wear down and discolor prematurely.
How to Fix It
Hand wash only. Let the basket cool, then soak in warm, soapy water. Use a soft sponge or nylon brush. The non-stick surface means food residue wipes off easily with minimal effort.
If That Didn't Work
For stuck-on grease, make a paste of baking soda and a drop of dish soap. Apply, let sit for 10 minutes, then gently scrub and rinse. It's more effective and gentler than dishwasher detergent.
Heads Up
The "Dishwasher Safe" claim is a marketing point for convenience, not a recommendation for longevity. Hand washing adds maybe 90 seconds to your cleanup and will extend the usable life of the basket by years.