Example Migrated from Codex:

Any allowable WP_Query parameters can be passed to wp_link_query_args. One example is filtering out post types:

Show only posts and pages

If you wanted only allow posts and pages to show up in the linked results, you could do something like this. In this example, we’re going to check to make sure we aren’t in the admin, so results would only be filtered on the front end, but admins could still add links to all post types.

add_filter( 'wp_link_query_args', 'my_wp_link_query_args' ); 

function my_wp_link_query_args( $query ) {
    // check to make sure we are not in the admin
    if ( !is_admin() ) {
        $query['post_type'] = array( 'post', 'pages' ); // show only posts and pages
    }

    return $query;
}

Remove specific post types from results

You’d use something like this if you only wanted to remove specific post types from the results.

add_filter( 'wp_link_query_args', 'remove_these_post_types_from_wp_link_query_args' );

function remove_these_post_types_from_wp_link_query_args( $query ) {
    // this is the post type I want to exclude
    $cpt_to_remove = 'article';

    // find the corresponding array key
    $key = array_search( $cpt_to_remove, $query['post_type'] ); 

    // remove the array item
    if( $key )
        unset( $query['post_type'][$key] );

    return $query;
}