I'm trying to keep things open ended so far, and see where it will go. But of course it needs some direction, too! So with that in mind...
It makes complete sense that there would be some, if not many, who would be scandalized by the presence of Kitherit as a "half breed". Keep in mind that it is quite rare for a half-elf child to survive birth. So this would be a unique situation for their society to deal with. Kitherit will, for the most part, look like a full blooded elf. A few minor differences would be that she is perhaps not as graceful as her kin, not just due to her human blood, but due to the fact that she was raised by humans. (Being less then graceful as compared to the rest of her race also gives me something to play with to keep things interesting.) Where most elves are more slender and fine boned, she may be just a bit more rounded and just a hair stockier, comparatively speaking.
The Ranger in question would indeed be an Elvish character, yes. Rishana mentioned them first, and I took it to mean someone who scouts the area looking for danger, a guard kept on look out for any danger that may encroach on Elven lands. Something else to keep in mind is how the role of a ranger may affect the opinions and feelings of your character (assuming you go that route). He would have had many interactions with humans, and I could see his opinions going one of two ways. First he may have come to loathe humans, and hate and distrust them on sight. On the other hand he may have had time to get to know them from a distance, understand their ways, and feel some sympathy towards them. He would have interacted with humans more then most elves.
On seeing Kitherit he would probably be most likely to recognize the subtle differences that point to her being half human. It's your call as to how he will respond to her.