Hi, Since you say White Paradigms, I assume you're saying the grillcloth is white then?
The thing I'd be most worried about, would be bleed-through, if the grill cloth is white color.
As another mentioned, some homemade concoction with a upholstery cleaner shampoo mixed with Oxy Clean.
If the Grill Frames are a painted wood (Such as are on my Vintage JBL Jubals, as they are either flat black paitned plywood I believe), one must try to dry them as quickly as possible with clean dry towels to prevent bleed through-staining onto the grill cloth.
To apply, I'd use something like a very soft fingernail brush-small soft brush, and if the cloth is glued to the frame, I wouldn't soak too much in this area for fear of the grill cloth coming undone.
If your Frames are Plastic, then Bleed through shouldn't be a problem. Whatever cleaner you use, I'm sure it will be important to make sure all of this cleaner is off the Cloth, otherwise you may see streaking-chauking.
Worse come to worse, and you're still not satisfied with the results, then the best bet for a fresh look might be new cloth?
While there are some that specifically sell acoustical grill cloth, you may be able to find a suitable replacement at a good fabric shop that will probably work just as well. In earnest, virtually all grill cloths do dampen the sound, and all speakers sound better with them off, but then this can possibly subject the drivers themselves to dirt, dust, and curious fingers/hands. mark