Can't believe no-one has pointed this out. Under TeamViewer's licencing model, it's perfectly fine to have Personal/Non-commercial selected on the client-side computer. In fact it's what they tell you to do. It's the machine that you use to access the clients that has to have a business licence.
And incidentally, TeamViewer monitors your usage (connection is managed via their servers, remember) so if you don't can a commercial licence and you remote control too many client PCs (no idea what their definition of 'too many' is) they start cutting you off. At first it's for a minute at a time, then they allow you to reconnect for five minutes and cut you off again, but if you persist the breaks get longer and the intervals shorter until you can't get any work done at all.