I have spent most of my working life being involved in the British Loudspeaker Industry.
A grill covers effect on sound quality depends mostly upon the design of the grill frame, this frame can alter the sound wave depersion. Grill cloths made from todays modern fine weave can have a small effect, but most manufactures will tailor the design of the loadspeakers frequency response with the grill fitted as this is the way it would normally be used.
As already mentioned having a grill cover is the best of answer to stop poking fingers and help to eliminate dust.
The best way to keep a grill cloth clean is a new paint brush.

Graham UK