This topic has come up before. Here's your solution!
Go to the grocery/drugstore and buy a liter of Murphy's Oil Soap.
I used to have a car detailing business and discovered that
Murphy's Oil Soap is better than 99% of the cleaning agents.
It has the ability to get into the tiny crevices and remove all grime.
Pour some oil soap into a bowl with some warm water.
Use a soft kitchen sponge with the solution in your right hand,
and a dry towel in your left hand, to mask off the grillcloth
while you clean. It's best to remove the chassis so no moisture
comes in contact with the metal.
Murphy's Oil Soap! I haven't tried the Murphy's wet naps,
but I'd stick with the liter bottle.