use XML::Twig;

my $twig = XML::Twig->new(
    twig_handlers => {
        div => sub { 
            my $class = $_->att("class") // "";
            $_->delete if $class eq "topsearchbar";
        },
    }
);

$twig->parse_html(\*DATA)->print;

__END__
Each of the unwanted divs at this point
<div>starts</div>
with
  <div class="topsearchbar">
    and <div>ends</div> with
  </div>. 
They are on lines 16-25 of the file.