For the more stubborn items that still remain, take a section of heavy duty aluminum foil and wad it up into a ball. Do not compact it too much. You still want a rough, uneven surface. With the burners turned down to medium, use a pair of tongs to hold the aluminum and gently scrub the grates. Do not over do it and ALWAYS use long tongs to scrub the grates.
Additionally, remember to oil the grates prior to grilling to keep food from sticking.