What is the criterion for distinguishing between obsessive whispering (waswasah) and reality in matters of people's rights, and is it necessary to seek absolution if something was soiled or damaged and then repaired?

The criterion for recognizing Waswasa (whispers/obsessive thoughts) is knowledge, so refer to scholars for them to clarify for you the difference between Waswasa and that which has a basis in reality. If doubts and illusions become numerous, their cure is to disregard them and not pay attention to them. As for what occurred from you regarding defiling another's property, remove it and restore the item to its original state. You are not required to inform its owner or seek their forgiveness.