Wire-bristle brushes may seem like the simplest way to clean your grill grates, but the unintended results can be pretty devastating if a bristle dislodges and someone swallows it. It's actually a fairly common occurrence, but there are other ways to de-grime a grill when soap and water just won't cut it.
There are lots of grill-cleaning tools that don't have wire bristles. The Char-Broil has nylon ones, for example. The Brushtec Double Helix calls itself a bristle-free brush; it's made of twisted pieces of wire. The Woody Paddle is made of oak and coated with a food-safe mineral oil. There's also the GrillStone cleaning block, which is similar to a pumice stone. GrillFloss is a stainless steel, hook-like device that you use to along each rod of the grate individually. You can even use a ball of aluminum foil that you hold with long-handled tongs. Some people even swear by onions.
If you have a portable steam cleaner at home, you can use it to help remove food remnants. As you're steaming, you can use one of the tools above to scrape away all the gunked-on stuff.
If things are really gunky, you can whip up a mixture of ammonia, vinegar, water, and baking soda, according to Apartment Therapy. You stick your grates in a garbage bag with the liquid and let it work for 24 hours. Pull it out, hose it down, and it should be burnt crud-free. Boiling a pot of coffee and letting the grates sit in a container with the brew for an hour will also apparently do the trick.
To help keep your grill from getting food stuck on it anew, use the tools to clean the grates when the grill is hot but before you start cooking, then use a paper towel covered (but not dripping) with vegetable oil, held in long-handled tongs, and rub the bars.