You should consider anyone who ask you to use Teamviewer a suspicious person. Here is quick glimpse of what could happen if allow them to access your PC:
A friend has fallen foul of the scam and downloaded Teamviewer and allowed access to his PC and, god forbid, given his Cred Card details.
I have told him to stop his card immediatly and leave his PC switched off. What actions are necessary to ensure the security of his PC?
Shit like this can happen. And worse! Because most of use have bitcoin stored on our machines. Avoid this service like the plague!
I would rather not test it for free, even if Op would give me vouches. You shouldn't too.