What can happen when a bird flies into a jet engine?
 

Check out the video I was sent by a retired United Airlines 747 Captain. It shows what can happen when a bird flies into a jet engine. This particular engine was, fortunately, on the ground at a testing facility.

Could they put some kind of sturdy (yet lightweight) grate in front of the engine so that birds would just ricochet off of it? Or would that mess with the physics of the plane's flight?

Yeah I think Physics come into play there. I must admit, it makes me think a little less safely about flying.

Nope. Because at 500 mph the bird would pass through it anyway. Besides, it would increase the odds of more debris from the grate shredding the engine and causing a bigger malfunction (tragedy).