Check your local and state government codes on exhaust system required, read the details and understand them, if you still feel like your citation was unjust then challenge the citation in court. Better to get a jury trail than a bench trail, you will be defending yourself to the common man, not just a judge who can only see black and white. You might have a case, but most of the time a citation like that is a fix and dismiss ticket, have a shop write you a note saying the repair was made or there was never an issue, then see if they will drop it. In Texas a muffler is required, I will post the Texas Statute, I am sure your state has something similar.
§ 547.604. MUFFLER REQUIRED[0]. (a) A motor vehicle shall
be equipped with a muffler in good working condition that
continually operates to prevent excessive or unusual noise.
(b) A person may not use a muffler cutout, bypass, or
similar device on a motor vehicle.
Acts 1995, 74th Leg., ch. 165, § 1, eff. Sept. 1, 1995.