Perhaps you could use a vacuum cleaner attachment to suck the powder out?
Could you google the manufacturer and ask them how to get the grill off, or if they have thoughts as to how to remove it? I assume you have tried every cleaning spray and scratch pad on the planet already.
It would bother me too, to the extent that I would seek to replace it if nothing else worked. Would your landlord go halves, as presumably in his/her interest to keep the place looking good for future tenants?
Sorry, I don't have a magic solution, but someone else may?