I'm doing something very similar to what you're trying to do in a program I'm working on now. I used the insert and delete methods in Tk::Text to refresh the data I'm pulling down with LWP::Simple.

I add text using

$curval->insert('end', "$current\n", "reset");
[download]

and put all new text at the end.

And to delete

$curval->delete("1.0", 'end');
[download]

start with the first line, initial character and delete until the end of text.

Check those methods out and I think they'll do what you're after.

Hope that helps!