Once you have the table, you can build a tree and then call $table_tree->as_HTML:

use HTML::TableExtract qw(tree);
my $te = HTML::TableExtract->new();
$te->parse($string_of_html);

my $table = $te->first_table_found;
my $table_tree = $table->tree;
my $table_html = $table_tree->as_HTML;
print $table_html;
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You can also call tables() to get a list of all the tables and then put a loop around the above.

You need to have the optional HTML::TreeBuilder and HTML::ElementTable installed for this to work.