The letter from walmart threatening to sue you if you don't pay is a scare tactic with little to no chance that you will be sued. Several of my clients have received similar letters demanding payment as "liquidated damages" with threats to sue if payment is not made. I tell my clients to ignore the letter and not one has been sued. Besides, it would probably cost them close to $200 to file and have you served with little expectation of a return. In other words, it would be like throwing good money after bad.
Don't worry about the letter. It has nothing to do with the criminal case. I've never seen a retailer follow up with any civil action on one of those letters. Your only concern is the criminal citation. As long as you receive a deferred disposition, you can expunge the case from your record completely.
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I am going to advise you to not post connections that you may or may not have with a judge online where anyone can read. This can get you and the judge in serious trouble. I am going to tell you to hire an attorney that can help you with this problem. The letter from Walmart is most likely their civil fine for what you did. The problem with paying it without having any written agreement is that this can be used against you in a court to help them prove your guilt.
Answering this question does not create an attorney-client relationship. Legal advice has not been given. Also, this question and answer is posted on a public forum and therefore any attorney-privilege is waived.