Thankfully for Ginny, Arcturus didn't have any idea who she was. He might have guessed that she was a Weasley just based on circumstances and the way she looked, but he certainly wouldn't care either way. What did he know about the Weasleys? Not much. That they had red hair, to start. He knew that he and his Uncle had picked on one of them in the library a few days back. Other than that? They were pureblooded. Who cared? He certainly didn't. Now, if he was told that she was Harry Potter's ex-fling, she'd become a whole lot more interesting. But Arcturus didn't know any of that.
"I don't have something from the kitchen because there isn't any meat in there quite... raw enough, for my tastes." That smile grew a little bit and turned into a smirk as he looked over his shoulder at the rabbit on the ground, fur and skin still attached to the animal. "If you would like some, I'm willing to share." Said as he looked back at her, only making the statement because he was sure that she would decline.