When you are editing a comment in Drupal, there is not delete option in the form.

To create a delete link, we have to theme the edit comment form.
1. Implement the hook_theme() as follow.
/**
* Implementation of hook_theme().
*/
function <module_name>_theme(){
return array(
'comment_form' => array(
'arguments' => array('form' => NULL),
),
);
}
2. Add the following theme function in the theme template.php.
/**
* Theme the output of the comment_form.
*/
function <theme_name>_comment_form($form) {
$delete_link = "";
if (user_access('administer comments') && user_access('post comments')) {
// Enable the delete link only with the above permissions
if (!empty($form['cid']['#value'])) {
$delete_link = '<a href="/comment/delete/' . $form['cid']['#value'] . '">Delete</a>';
}
}
return drupal_render($form) . $delete_link;
}
3. Clear the cache and try editing a comment. The delete link is ready now.

This post is based on an article by Tom Kirkpatrick about customize the edit comment form in Drupal 6.
System Seed – How to customise the comment form in Drupal 6. Thanks Tom.
Done =)
Reference: System Seed – How to customise the comment form in Drupal 6
