Thanks. Good input from all and fast response from Moderator/s, thank you.
Just to clarify, 6.10.10347 doesn't (ever) stop the TeamViewer service; it only starts it when it's set to Manual but not already running. It then leaves it started and running, no reversion.
Some more fun-facts I've just discovered by playing around ....
1. When TV's Service is set to Manual, TV itself doesn't actually bother to start it when it, TV, starts. I ran TV for a while making and ending connections and at the end of all that, its Service was still not running (and still set to Manual of course).
2. If TV's Service is set to Disabled (as opposed to Manual), 6.10.10347 doesn't manage to overcome that and start the Service. That would have been even more impressive and a tad more scary.
3. I confirm that if TV (i.e. TV itself, not its Service) is running when CCleaner is initiated, it is in the category of things like browsers and W Explorer etc that CCleaner would either like to have closed or it will skip them on that run. Interestingly, there are plenty of things, some surprising, that are not in this category ... eMail clients, image viewers, media players etc, including some things that are selectable as applications to be cleaned by CCleaner e.g. VLC, MS Office etc, that CCleaner doesn't care if they're open/running when it's doing its thing. I've never quite got my head around how this works, what's in or out, but I don't need to know.
I think that's it. Cheers to all from Sydney Aust.