Remove post format anchor element and silence image alt attribute

functions.php

<?php

//  remove the default Genesis core callbacks
remove_action( 'genesis_entry_header', 'genesis_do_post_format_image', 4 );
remove_action( 'genesis_before_post_title', 'genesis_do_post_format_image' );

//  add custom callbacks
add_action( 'genesis_entry_header', 'custom_do_post_format_image', 4 );
add_action( 'genesis_before_post_title', 'custom_do_post_format_image' );
/**
 * Add a post format icon.  
 * 
 * ** Modified Genesis core genesis_do_post_format_image() function. **
 *
 * Adds an image, corresponding to the post format, before the post title.
 *
 * @return null Return early if post formats are not supported, or `genesis-post-format-images` is not supported
 */
function custom_do_post_format_image() {

    //  if on a page, return (do not display icon)
    if( is_page() )
        return;

    //* Do nothing if post formats aren't supported
    if ( ! current_theme_supports( 'post-formats' ) || ! current_theme_supports( 'genesis-post-format-images' ) )
        return;

    //* Get post format
    $post_format = get_post_format();

    //* If post format is set, look for post format image
    if ( $post_format && file_exists( sprintf( '%s/images/post-formats/%s.png', CHILD_DIR, $post_format ) ) )
        printf( '<img src="%s" class="post-format-image" alt="" />', sprintf( '%s/images/post-formats/%s.png', CHILD_URL, $post_format ) );

    //* Else, look for the default post format image
    elseif ( file_exists( sprintf( '%s/images/post-formats/default.png', CHILD_DIR ) ) )
        printf( '<img src="%s/images/post-formats/default.png" class="post-format-image" alt="" />', CHILD_URL );

}