20,000 lines is not likely to be more than 2M or so. That is not so big as to prevent slurping on most machines. The 40-some phrases in the junk file are insignificant in size, so lets compile them just once.

use Fcntl ':flock';
my @regexen;
{
    open my $rx, '<', '/path/to/junk.txt'
      or die $!;
    @regexen = map {
        chomp;
        qr/\Q$_\E/
    } <$rx>;
    close $rx
      or die $!;
}

for (@list_of_files) {
    local $/;
    open my $fh, '+<', $_
      or warn $! and next;
    flock $fh, LOCK_EX;
    my $contents = <$fh>;
    # study $contents;  # may want to try this
    $contents =~ s/$_//g for @regexen;
    seek $fh, 0, 0;
    print $fh $contents
      or warn $! and next;
    close $fh
      or warn $! and next;
}
[download]

That should give decent performance. I've locked the file after opening to read and write, so you are protected from races.

Update: MidLifeXis' reply reminded me to chomp before compiling the regexen. Added to code, along with revised error handling in the big loop.