Hide/disable EDIT & DELETE links in menu-customize form
You can create a small custom module and implement hook_form_FORM_ID_alter().  Below is a quick example for Drupal 6:

.module file

&lt;?php
/**
 * Implementation of hook_form_FORM_ID_alter()
 */
function YOURMODULE_form_menu_overview_form_alter(&amp;$form, &amp;$form_state) {
  GLOBAL $user;

  // Check if user has a certain role or not and menu is primary links
  // Change ROLEID to the role id you want operations hidden from
  if (!array_key_exists(ROLEID, $user-&gt;roles) &amp;&amp; arg(3) == 'primary-links') {

    // Hide edit/delete menu operations
    foreach ($form as $key =&gt; $ele) {
      if (substr($key, 0, 5) == 'mlid:') {
        unset($form[$key]['operations']);
      }
    }

  }
}


Change YOURMODULE to the name of the module you are creating.  For assistance creating custom modules, see the Module developer's guide.  

To work in Drupal 7, I believe all you would need to do is change arg(3) to arg(4) due to the path changes.