I would not use Tie::File unless there is some user requirement of which I am not aware.
I would read the input file into memory, save input file as a backup, modify input file as in memory, write modified contents to the output file.
Untested, but hopefully gets you on the right track...

use strict;
use warnings;

my $inDir =".";

my @inFiles = glob ("$inDir/*.txt"};

foreach my $infile (@inFiles)
{
   # read infile into memory..
   
   open IN, '<', "$inDir/$infile" or die "$!";
   my @lines = <$infile>;
   close IN;
   
   # save the original infile
   
   rename ("$inDir/$infile", "$inDir/$infile-backup") or die "$!";
   
   # modify the data that's in memory
   
   unshift @lines, "whatever_you_want\n";
   
   #save the new data into the original file name
   
   open (OUT, '>', "$inDir/$infile") or die "$!";
   print OUT @lines;
   close OUT;
}
[download]

There are issues when "something goes wrong" and Tie::File. The above saves a "backup" in the case of problems.