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I think that by "modify" they actually don't want you to mess about with the parameters that the script passes back to their server. Many counter scripts sniff the referrer, browser, OS, resolution, and a whole load of other stuff.
You could modify the script to falsely claim that all your visitors use Mozilla for example. That sort of change would get you canned.
Making a change, to validate the code is unlikely to cause you a problem. However, I would send the counter script author (as a "concerned surfer", and using some anonymous "throw-away" email address, from a different IP address to your normal one) a note to say what needs to be changed.