How do I alter the options in the add menu link checkbox in the node edit form?
$form['menu']['link']['menu_parent'] is the form array select box for the menu selector widget. $form['menu']['link']['menu_parent']['#options'] contains the key/value pairs for the menu select box. 

In your given example, you can use unset($form['menu']['link']['menu_parent']['#options']['my_uneeded_menu_id_option']); to remove your  unneeded menu items.