Well Jim,
This is kinda funny and or interesting. Glass is not penetrable, for the most part anyways. Can it be stained, well, yeah it can but, I would definitely think, NOT BY A BIRD STRIKE. Anyway, I've used actual rubbing compound and or polishing compound on my windshields in the past. There's zero damage and, in actuality, the glass is a tad smoother so, the wipers just sort of glide right over when it rains. But, if you can get your hands on some 3M rubbing compound, and a machine (not one of those cheesy random orbital $29.00 ones either), I'd bet the farm you'll lose that bird strike evidence.
Scott