Teamviewer is fine if you don't mind a whopping great tunnel into your network to servers in germany.
I'm not worried about it, you should see how many times a day my office server gets randomly pinged by servers in Russia or East Europe (and it's not listed anywhere and our IP usually changes every 2-3 months), they then procceed to randomly access a wide variety of ports before they get shut out for too many failed attempts (or too many too fast).
Imho, they know about the door already or one of their snoopers will shortly, it's all about the lock (and boobytraps) you have on the door and behind it that really matters.
And as I said, microsoft comes with a similar RD program these days (I think starting with XP it was standard issue for a while and may still be, but I'm not a windows guru), doesn't matter if you have TV or not, they get into your door they can control your PC.
Your computer is at risk as soon as you plug it into (or wirelessly connect) a network/internet, it really is that simple.
I use Citrix Gotomeeting myself. It's more convenient than Teamviewer as it installs automatically through browsers. Teamviewer is annoying with its version limitations, if your client has a newer version installed than what you use, teamviewer refuses to work with the older version. Then you're going to either pay 1500 bucks for a new version for nothing, break the EULA or use something else. I use something else.
This is why I love TV6 and hate TV7 (and still preffer using TV6), TV6 was a lot more tollerant of connecting with older or other TV6 clients. It would try to make due and it usually would work. Also TV6 didn't like resetting passwords everytime a neighborhood dog lifts its leg to one of our distribution boxes.
Find an old version of TV6 and downgrade imho if you can.
And yeah, windows actually did it right with their RD - lightweight, basic, simple, reliable.... why can't their OS guys get it? lol