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What this is showing you is what IP addresses have been assigned to each computer. Most routers so not keep a log of sites visited - in fact, those that do (usually business firewalls) have logs that are cimberrom to pour through. It's not nearly as easy to accomplish as it seems it should be. The challenge is that the counter actually makes thousands of outboint connections in a minute. Even connecting to a single web page causes hundreds of connection requests for elements of a page. So it is generally just not practical to do. And home routers don't have the capacity to strore the logs that would result.
But there are various softwares you can run like Net Nanny that will restrict and track child behavior on the computer itself.
And that is something they cannot delete.