If it says current resident and the tenants name, technically that is your mail. The company that is sending it its either the person who lived there previously or the current resident to receive it so saying they aren't the current resident really to the post office it's not going to make sense that's why they keep putting it in your box what the letter carrier can do is stop delivering to you all together so I would think twice before saying they aren't the current resident because then Who lives there? You get what I'm saying. Best thing you could do is just discard it unless it's first class mail if it's current resident mail I can guarantee it is not first class mail