This exact scam was thoroughly investigated on a podcast called Reply All a few weeks ago. The company that runs it is out of Delhi. You should know better when they start asking and saying completely stupid things. You may have already been had.
wish I had seen info on that. Like I said, they had so much exact information that they convinced me that they were the company I dealt with last year to help me with computer work.
Good point. While TeamViewer was active they could have been downloading files from the computer and looking for lists of accounts and passwords.
I hope TeamViewer is not giving access to your computer every time you turn it on.