Here is an easy and simple solution for your problem. If your child is smart, though... it might not work.
All you have to do is screw up the masters.cfg file in the teeworlds directory.
Simple Way
1. Navigate to: C:\Users\<Username>\AppData\Roaming\Teeworlds
2. Delete the masters.cfg file. Do not run Teeworlds until you have finished the rest of the steps!
3. Download this custom masters.cfg and copy it to "C:\Users\<Username>\AppData\Roaming\Teeworlds".
4. After the copy has completed, make sure that your children (hopefully younger than 10) do not know of this special folder (data directory).
5. Run Teeworlds. Under the internet tab, the server list should show Refreshing Master Servers. Then, after realizing that the edited file had given it broken links for the server list, it should say "No Servers Found".
Well, I wrote this because I didn't really understand Kottizen's way.. but he's more experienced than me, so I probably am just too young to learn his more advanced ways.