Haha. Join the club! I understood that the brother killed the bird and said as much. What I didn't understand, and would be grateful if someone could explain is, WHY? It was something to do with betting (horses?) and money? But I didn't understand whose money it was and the whole thing. And the note? Who was the note from and what did it mean?
Jud gave Billy the note (containing the name of the horse) and the money to place the bet on the horse. Billy spent the money instead, the horse won (so Jud would have got a fair bit of winnings), so as a punishment (because he couldn't find Billy), Jud killed the bird.