When I have grease on my kitchen cabinets I will use vinegar to clean the grease off the kitchen cabinets which works very great and is not a harsh chemical.
Just take a clean cloth or sponge and pour some undiluted vinegar onto the cloth or sponge and wipe down the greasy cabinets to remove the grease.
Then after wiping down the cabinets to remove the grease with the vinegar you then take the cloth or sponge and rinse it off and then use a damp cloth or sponge with water to wipe the vinegar and grease off the cabinets.
If you constantly wipe the cabinets down regularly then it will take less work to clean grease off the cabinets.
Pine Sol also works great at removing grease from kitchen cabinets and other wood furniture or use some Simple Green or other degreaser such as Purple Power to remove the grease from the kitchen cabinets.