Don't contact them at all. I generally advise my clients to ignore these civil demand letters. You don't owe them anything, especially if they got the item back. In order for you to owe them anything they would have to sue you and win. To do so would cost them substantially more than they can ever hope to recover (and they would have to prove damages) so they usually don't pursue it. They send out these letters because it doesn't cost them anything and they are hoping that you don't know better and simply send them money. Ignore it.
I don't have experience on the debtor's side, but I have had some clients who have sent out these demand letters with a collection attorney.
Some retail companies, such as Kohls, send demand letters to people who have been caught shoplifting in their stores, or to parents of young people who have also been caught. In most cases, the store has recovered the items stolen and therefore, is not claiming the value of what was taken.
The letters are often signed by a lawyer and demand payment of amounts in the the range you describe called a "Civil Recovery” for what they claim to be the costs of detecting shoplifters in their stores. The letters sometimes suggest that if you don’t pay by a certain date the amounts will increase.
The letters themselves are not the same as a court order. You can choose to pay the amount or not. If you do not pay, the store *can* start a lawsuit. However, that it is rare and you have a defense, as you stated. The attorney in your letter appears to be a New York attorney, and not a Connecticut one.
So, you can choose to ignore the letter, or if you feel morally obligated, you can pay it. If you do pay it, you should get a release. If you get a small claims notice of suit, do NOT ignore that. Good luck and stay safe.
**Disclaimer: Charles F. Basil is licensed in CT only. Any opinion given is based upon the general principles of law, but local laws may vary. This opinion is given for informational purposes only, and no attorney client relationship has been formed. Opinions on a website can not and should not supplant the advice of an attorney presented with all of the facts in your jurisdiction.**
As does Mr. Lieberman, I generally advise clients to ignore the letters. Not because the store won't file suit due to costs as some states provie for the ability to recover attorney fees and costs of suit but because the store cannot prove damages.
I also agree with Mr. Basil's caution about NOT ignoring a small claims complaint.
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.