Normally, a civil demand letter would not show up on a credit report, which is likely what your lender will review when you buy a home. However, if the debt and demand is based on contract, the creditor may be able to report you to a credit bureau. It sounds like you have a civil demand based on an alleged crime. If there is merit to the charges, a settlement may protect your future. The merchant could still press for charges to be filed, and if they can get a letter to you they can get enough information to law enforcement to charge you with a crime. Law enforcement can get your social security number. If you are buying a house, and there is merit to the allegations, paying the demand could be a small price to pay to protect yourself. However, if there is no merit to the charges, you may want to respond putting it on record that you did not commit the charges. If you are charged criminally, the judge could order you to pay the amount as restitution and you will have to pay the $250 and have a criminal record. I have known of businesses to make a civil demand on shoplifters to cover their losses and give the perpetrator an opportunity to avoid prosecution. You need to consider the merits and the risk of a future criminal prosecution in deciding how to respond.
This answer is for general discussion purposes only, and my answer does not create or imply an attorney-client relationship between the questioner and me. I do not represent any person without a conflict check and written agreement.