To clean a greasy hood filter, The Kitchn recommends using a mixture of boiling water, dish soap and baking soda, along with a scrub brush and paper towels. It is possible to clean the filter in the dishwasher, but it is best to do it by hand the first time.
Fill a bucket or the sink with boiling water, and mix-in a squirt of dish soap and a quarter cup of baking soda. Let the filter soak in the water for 10 minutes, and then scrub the filter using more dish soap. Rinse the filter, and dry it with paper towels to complete the process.