One way to do this would be to simply hide the upload/insert media button: and, then add featured image support for your themes posts, so a user can still attach images to the post.
Hide upload/insert media button for your theme in: functions.php:
function hideUploadInsert($hook)
{
if($hook != 'post.php' AND $hook != 'post-new.php')
return; // if not in the edit or new admin pages, for Posts or Pages, then do nothing.
echo '<style type="text/css" media="screen">
#wp-content-media-buttons {
display: none;
}
</style>';
}
add_action('admin_enqueue_scripts', 'hideUploadInsert');
Add featured image support to your themes posts in: functions.php
add_theme_support('post-thumbnails', array( 'post' ));
EDIT:
I didn't realize you were referring to attaching multiple images to a post. You could just use the css I gave above to hide the button for inserting images into a post: and, then use one of the plugins that come up in a google search for attaching multiple featured images to a post:
https://www.google.ca/search?q=wordpress+multiple+featured+images
pre_save_post
and strip those tags, but I think you're better off simply disabling all unwanted TinyMCE buttons.