Replace WordPress HTML output with New function

It’s hard to say without more details. Which functions are you referring to?

Thanks Otto. Here are the functions

function do_settings_sections($page) {
    global $wp_settings_sections, $wp_settings_fields;

    if ( !isset($wp_settings_sections) || !isset($wp_settings_sections[$page]) )
        return;

    foreach ( (array) $wp_settings_sections[$page] as $section ) {
        echo "<h3>{$section['title']}</h3>\n";
        call_user_func($section['callback'], $section);
        if ( !isset($wp_settings_fields) || !isset($wp_settings_fields[$page]) || !isset($wp_settings_fields[$page][$section['id']]) )
            continue;
        echo '<table class="form-table">';
        do_settings_fields($page, $section['id']);
        echo '</table>';
    }
}

and

function do_settings_fields($page, $section) {
    global $wp_settings_fields;

    if ( !isset($wp_settings_fields) || !isset($wp_settings_fields[$page]) || !isset($wp_settings_fields[$page][$section]) )
        return;

    foreach ( (array) $wp_settings_fields[$page][$section] as $field ) {
        echo '<tr valign="top">';
        if ( !empty($field['args']['label_for']) )
            echo '<th scope="row"><label for="' . $field['args']['label_for'] . '">' . $field['title'] . '</label></th>';
        else
            echo '<th scope="row">' . $field['title'] . '</th>';
        echo '<td>';
        call_user_func($field['callback'], $field['args']);
        echo '</td>';
        echo '</tr>';
    }
}

Editing those parts of the core might be a *really* bad idea. Those are core parts of the Settings API, and plugins use them and expect them to behave in a certain way. Changing those will very likely affect how plugins settings screens work.

If you want to use a different method for displaying options in your own plugin or theme or something, you don’t really need to copy those functions to different names. Just make your plugin screen the way you want to make it instead of using those parts of the Settings API.