foreach $line ( <FH> ) {                
   if ( $line !~ /to=<.*(our\.domain)/i) {    
# our external domain is a subset of the ones we're looking for
        if ($line =~ /to=<.*\.gov>.*relay=localhost/i) {
            @ids = ($line =~ /\ ([0-9A-F]{11,12})/g);
            %msgids{$ids[0]} = $ids[1];
        }
    }
}  

open (FH2, $file ) or  die "Cannot open file 2nd time: $!";
foreach $line ( <FH2> ) {
    if  ( $line !~ /client=(ourhost1|ourhost2)/ ) {
        foreach $keys (%msgids) {
            if ($key =~ /$line/) {
                delete $msgids $key;
            }
      }
}
# then do something to run through the log again and print
# the delivery report line from the second msgid