Grease can be hard to remove from cabinet hardware but you can use an old toothbrush soaked in warm water and dishwashing liquid then scrub the grease spots with it. You can also soak rags in vinegar before wiping off the grease buildup if that works better for you. If your kitchen cabinets are made of wood, simply wipe them clean with a damp cloth.
If there is some dirt left on top of your cabinet handles after cleaning all that grease, dip a soft rag in white vinegar, then scrub gently at any remaining dirt until it's gone.