I'm a bit confused by what you're trying to accomplish here:

       $TheLine = $_;
          while (my $TheLine = <INPUT>) {
           # ....etc.
          }
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You're overwriting $TheLine with the default variable, "it" ($_) outside your loop and then creating another $TheLine that is out of scope (within the loop).

Here's one way of doing what I think you want. It's probably not the most advanced way, but I hope it makes sense and helps in your understanding of what's gone wrong.

      @lines = <INPUT>;
          for (@lines) {
             if (/<RD>[^\n]*Status Compendium<<.JL>/i ) {
             # notice that $_ is assumed here
               foreach my $word (@WordList) {
                 print OUTPUT if($_ ne $word)
                  # here we need $_ for camparison (?)
               }
             }
          }
[download]