Seems you have something plugin, that causes the problem, because WP doesnt put hidden anchors in the content. have you double checked the post-editor textarea (html/visual) to determine when that ..anchor..
appears?
however, i dont recommend filtering, instead, save the CORRECT CONTENT in the back-end, instead of filtering the incorrect content on front-end.
use something like this:
add_action('save_post', 'my_filter_func',1);
function my_filter_func($post_id){
if ( ! wp_is_post_revision( $post_id ) ){
$_POST['post_content'] = str_replace('<a class="anchor"> OR WHATEVER SHOULD BE THERE, '', $_POST['post_content']);
}
}