I believe New York doesn’t report traffic violations to other States unless you fail to respond to the ticket. I know NY doesn’t count points from any other US State but will suspend if you just ignore it (except from six States, including Michigan, which even if you ignore the ticket it they will not suspend your license.)
Your best bet is probably to mail it back guilty and pay the fine. It likely won’t affect you. If you want to play extra safe you can get a lawyer for about $400.