The function, the_meta() allows you to hook to the the_meta_key filter (which currently is not documented in the Codex); this is where it fires off:
// wp-includes/post-templates.php @line 744
echo apply_filters('the_meta_key', "<li><span class="post-meta-key">$key:</span> $value</li>\n", $key, $value);
http://core.trac.wordpress.org/browser/tags/3.2.1/wp-includes/post-template.php#L735
This filter is applied to each and every meta pair, which means that you can add a filter to suppress based on a specific key, value or key/value pair like so:
function wpse31274_exclude_my_meta( $html, $meta_key, $meta_value ) {
if( 'remove_this_key' != $meta_key )
return $html;
return '';
}
add_filter( 'the_meta_key', 'wpse31274_exclude_my_meta', NULL, 3 );
Tried and tested, seems to work, so I hope it helps.