Household Bank HSBC, Midland Credit Management, INC Will not disclose information reguarding debt los angeles, California

When I got divorced I started receiving settlement statements for HSBC in my name.

I did have previous debt to them that was paid off. I wrote them a letter requesting a signed document with my signature and past statements to get knowledge on what the debt was for. They had told me that they never received any letter. I mailed 4 of the same letters knowing that they would get at least one. They are putting negative remarks on my credit report because I am not paying until they can provide me any proof that I even opened this. Originally the debt was $9,000 then months go by I don not receive anything from them. Today I receive a statement for $4,421.82. I am truly confused how this is. How do I investigate something that I am not granted any knowledge of?