The civil demand letter is separate from a criminal offense. If they did not give you a ticket nor call the police & release you to your parents (if you are underage), then you are not being prosecuted criminally and it will not go on your record.
If you do not pay the demand, they have the OPTION of suing you. Many people do not pay, or pay a fraction and write "in full payment" on the check. I cannot tell you what to do but I can tell you that if you do not pay, you will not get a criminal case because of the non payment.
Well, it sounds like you were really lucky. They do have the option to sue you, but they have to prove damages pursuant to the statute and most of the time they (their legal department) understand that it is too costly to sue someone who apparently has no money anyway. If you received a tresspass warning, do not go back or you can be arrested for criminal trespass and taken to the county jail.