I guess I'm not totally clear about the problem here, but isn't what need to do here basically just
<font class="small">Code:</font><hr /><pre>#Insert some code that converts $DATESTRING into a numerical $DATE
if $DATE + $CUTOFF < $TODAY; then
rm file_$DATESTRING.tgz
fi</pre><hr />
At what step in this process are you having trouble?
Edit: Or yeah, just use a built in linux function that does all the work for you.