As I am in laundry and dry cleaning business, I cater to many high profile clientele in Mumbai, who need detail cleaning of their expensive vintage canvas, lampshades etc. I highly recommend you to dislodge the grill and use a soft bristle paint brush and a clean soft shoe brush to vibrate the dust of as gently as possible, thoroughly from inside and outside without missing any corners.
The next step would be to use a dry vacuum with a soft bristle adaptor for suctioning of the loose dirt from the grill. The result will be near 60% appreciable.
For those who have a wet and dry vacuum, I suggest you to buy a Dry Foam Shampoo can mostly available in malls having large stores, or in automobile accessories stores that sell such products to clean the car upholstery. Just spray over all the exterior grill area, then give a light soft bristle scrub and vacuum gently. After this process is complete either keep in the shade or use hair drier on low heat till dry.
Even if you cannot find a dry foam shampoo can, then try this home method. Use your hair shampoo. Just 1 tea spoon in mild hot water. Beat like the way you eat an egg. Let the foam gather, Gently lay that foam all over the grill and scrub gently. Later use only wet and dry vacuum ONLY. REMEMBER do not use dry vacuum to suction any thing moist, as you will end up charring your vacuum motor
You certainly will have a new laundered grill. Please do reply if you are happy with my suggestion
