It's a common scam.
Im glad to read you stepped away. Some folks go through the process allowing these individuals access and now effectively have to bin the PC as there's no way of knowing what's been installed, changed and manipulated.
Just had an enjoyable conversation with her husband / brother / cousin etc and I was most certainly impressed with how concerned he was with how to protect my internet security and what he knew about operating computer systems. Telstra knew I was having a problem which could be shown by the flashing lights on my main router but he would step me through the solution so nobody could get in and steal my identity, which would leave me liable for any damages caused by use of my internet account. How kind of him to fix my problems at no charge and didn't even have to prove I was the account holder which I'm not!!
It was what he didn't know that was his undoing as I have been networking computers for nearly 40 years and know that my router(s) lights are meant to flash occasionally. I was only following all his instructions disconnected from the internet so he couldn't hurt me.
It was his request to type www.bit.do/connecttelstra then hit enter that blew it, as when I said to him that the link, while seemingly from Telstra, looked highly suspicious and perhaps he get Telstra security to actually write to me about the "problems" I was having, HE HUNG UP ON ME!!
The link is actually a shortened url to https://dl.tvcdn.de/download/TeamViewer_Setup.exe and so if you click on OK, you will give away FULL access to your computer for their nefarious doings, so beware.
Tomorrow when his other cousin rings back, I'll be on my Linux computer so will see how far this goes.