How To Remove The “Click here to cancel reply” Link From The WordPress Comment Form

add_filter( 'cancel_comment_reply_link', '__return_false' );

See /wp-includes/comment-template.php#function get_cancel_comment_reply_link() for more background.

But if you do that the reply form will not move to the comment. The more interesting question is: Why doesn’t the link work for you? Do you have this line in your footer?

is_singular() and get_option( 'thread_comments' ) and wp_print_scripts( 'comment-reply' );