Well sure, the area right over the heat will be "cleanest" (and therefore, rust soonest from lack of grease ... ). Maybe this is just semantics, but these sorts of nickel-plated steel grates can not get "seasoned" in the way raw iron (cast iron) or raw steel (carbon steel) get and need to be seasoned.
With these nickel plated grates (where the nickel plating never lasts ...) keeping grease (or veggie oil, or whatever) on them is critical.
So, then:
1) Rotate the grate with subsequent uses so that the same section isn't always over the heat. That'll help it from rusting there. And toss a little oil on it.
2) A metal scraper of some kind, as Gummi suggested, will clean the crud from the tops of the grate tines so that flecks don't get on food.