We've got a canned response that says:
This ticket has now been closed. Please do not reply to this message unless you believe the issue hasn't been fixed, as doing so will reopen the ticket. If you'd like to report a separate issue, please do not reply to this message either. Instead send a new message to [support email address] to open a new ticket.
It's mostly fixed the problem, although there are inevitaby still a few people who don't read it and reply with "Thanks" anyway. Not so many to cause a big issue now though. It would be nice for osTicket to have a different template when a ticket is closed, but it's not that big a deal really. We couldn't just ignore any replies to a closed ticket unfortunately, as not only is there the obvious scenario of people replying to say "Hey, it's not fixed!", but we get some people replying to old tickets with a new response just because they can't be bothered typing out a new email.