Your telnet cmd is interacting with ksh, not perl, at the other end. So you need to tell it to run something. You could, for example, tell it to run:

@contents = $telnet->cmd(qq(perl -e '$,=$/; print stat(shift)' $logfil
+e));
[download]

But if you only need mtime, you could tell the remote perl to just return that.

@contents = $telnet->cmd(qq(perl -MFile::stat -e 'print stat(shift)->m
+time()' $logfile));
[download]

Hope that helps.