I recently had to remove link elements from a feed URL, and trying to avoid setting up basic WordPress features, the following solutions work.
Make sure you have the functions.php file in your directory with the one you are using. If you do not create a file and edit the file. The following lines will help remove the selected lines from your wp_head() function:
<?php remove_action( 'wp_head', 'feed_links_extra', 3 ); // Display the links to the extra feeds such as category feeds remove_action( 'wp_head', 'feed_links', 2 ); // Display the links to the general feeds: Post and Comment Feed remove_action( 'wp_head', 'rsd_link' ); // Display the link to the Really Simple Discovery service endpoint, EditURI link remove_action( 'wp_head', 'wlwmanifest_link' ); // Display the link to the Windows Live Writer manifest file. remove_action( 'wp_head', 'index_rel_link' ); // index link remove_action( 'wp_head', 'parent_post_rel_link', 10, 0 ); // prev link remove_action( 'wp_head', 'start_post_rel_link', 10, 0 ); // start link remove_action( 'wp_head', 'adjacent_posts_rel_link', 10, 0 ); // Display relational links for the posts adjacent to the current post. remove_action( 'wp_head', 'wp_generator' ); // Display the XHTML generator that is generated on the wp_head hook, WP version ?>