If the text file could be large, consider

open (IN, "<grep");
my %lines;
while (<IN>){
  $lines{$_} = 1;
}
close IN;

open (OUT, ">gout");
# assumes input data comes from stdin
while (<>){
  print OUT $_ if exists $lines{$.};
}
close OUT;
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Untested, but I think I got it right. Save the small stuff, not the big stuff.