I would not worry about it too much. You can get a grill thermometer to check the temperature of the surface to make sure it is not too hot. About 300-350 is fine. The grill I worked on for years did the same thing. I just cleaned it every night so it did not build up. My friend at a different restaurant always kept his shiny while cooking but we never figured out why his and not mine.
Cooler temperature, closer to 300 might be the answer but the food takes longer to cook.
In either case, it won't affect the food. Keep scraping any residue off the grill so one thing does not taste like another but otherwise it's just a pain to clean.