I have to agree a complete rebuild as malware / virus writers work hard to try and make their illegal software as difficult to detect as possible and no anti-malware / anti-virus is 100% in detecting them.
Personally, I think they should be shot in front of their families, along with hackers and spammers, that would deter the lying, cheating, thieving scum.
Personally, if it was me, I would also report it to trading standards and the police and your telecoms company, who must know where the calls originate from. The police now have a dedicated unit for dealing with IT crime and the more information they have the more likely they are to act to close it down.
You also need to cancel the debit / credit card so they or other 3rd party criminals don't (where they sell on the details) go on a spending spree with the information. To turn cards into cash they use bank account mules. I'm sure we have all had the earn money by collecting and transferring money using your bank account spam emails, the desperate and the gullible then become account mules.
Unfortunately, where many call centres are in India and other low cost countries, there are security problems with data theft common where employees are in a low paid job, so they sell on the customer data to make extra money. This has in the past included from BT although they have always denied any problems, which I know from experience where I had phone call from a scammer that have known too much about my BT account to not have got inside information.
Remember, NEVER EVER, give any bank account or credit / debit card details or other financial information of any sort to anybody you don't know that calls you, whoever they say they are from, as they could be anybody from anywhere.