I wish to remove, disable or hide the comment authors’ links to their sites from my home page

by

Add following code snippet in functions.php. (in your themefolder)

Edit new code:
– This should do the trick, sorry for the delay.

/**
 * Remove post author link on comments
 * 
 * @return string $author
 */
function wpse218025_remove_comment_author_link( $return, $author, $comment_ID ) {
    return $author;
}
add_filter( 'get_comment_author_link', 'wpse218025_remove_comment_author_link', 10, 3 );

Note: you can add functions almost always to your functions.php in your theme folder. Ofcourse is it also possible to make a plugin but that needs a little more coding.
Please take a look here for making your own plugin.