(NJ) Accidental Theft Advice

Earlier today I went to pick up a prescription from Wegmans. I decided I would pick up a sub from their sub shop whilst making my trip there, saving me time, so I may get to class on time. Grabbed my sub, and headed over to the pharmacy on the other side of the store to grab my prescription, where I was told there was a technical difficulty with my insurance and that they needed some time.

After about 20 minutes, I started to worry that I was going to be late for class and the fact that our professor was going over midterm material did not make matters better. Finally she called me over and told me I was ready to go. Sub in hand, I quickly headed over to the terminal where she was going to ring me up. I put my sub on the counter, scan my apple pay, initial the box, grab the prescription and sub and swiftly walk out the automatic doors. 10 step from the door an older guy stops me and pulls a laminate ID from his shirt and says, "come with me". Startled I ask, "What seems to be the problem?", he then looks at the sub and back at me. Immediately I blurt out, "Oh no! I had absolutely no intention of stealing this." (Yadda yadda, you get the point.)

After about 20 minutes of trying to defend myself, explaining I used to work for Wegmans and that I knew the manager of the front end (currently working, whom he called in and I could tell on his face did not believe that I had any intention to steal it, then was used as a witness), he did not budge or accept the fact that I made an accidental mistake. He just filed the paperwork, and had me sign a civil demand notice to the amount of $158.99 ($8.99 for the sub and $150 for the civil penalty) and a warning that I would not be allowed to enter the store for 2 years from this date, or the police would be called. He then sent me on my way, no other words, just the disappointed look on my ex-co workers face.

So now the question of the matter: Do I try to fight this by going to corporate and explaining that this was just a mistake and that I had no intention of stealing this sub, or do I just suck it up and pay the civil demand payment?

TL:DR; Accidentally stole a sub from Wegmans, absolutely no intentions, I used to work there, many friends and family work and shop there. Given a Civil Demand Notice of $158.99 ($8.99 for the sub and $150 for the civil penalty) with 20 days to pay it off. Do I try to fight it by going to Corporate or just suck it up and pay it?