Does a sin or something that requires atonement remain upon me after the court acquitted me in the case of accidentally killing an old woman, and her son refused blood money, preferring to receive insurance compensation?

If there was no negligence on your part that led to the accident, such as having taken safety precautions and adhered to traffic laws, and then the accident occurred, then you are not liable, and the court is correct in acquitting you. However, if you were negligent in something that led to the accident and the court was unaware of it, then your conscience is not absolved from the blood money (Diyyah) and expiation (Kaffarah). Likewise, if the court's ruling was a flawed secular judgment, or you obtained the verdict through bribery or favoritism, then your conscience remains burdened with the expiation. The blood money is obligatory upon the 'Aqilah (male relatives on the father's side), and if they do not exist, then it is from the public treasury (Bayt al-Mal), otherwise it is from your own wealth.