While it's impossible to take out the exhaust fan completely due to structural limitation, there is a way to clean the clean the protective cover and the fan blades.
Please follow the steps below:
1. Remove the 5 screws as shown below: 3 on the top, 2 at the bottom.
2. turn over the fan, remove the 4 screws on the back,
3. Separate the fan cover and the fan, do a thorough cleaning.
Related post: Fans Cleaning Guide