I found the problem:
The display function I was using contains two sub functions that are normally needed to display text in my web pages.
function forDisplay( $text ) {
$text = htmlentities( $text );
$text = nl2br( $text );
return $text;
}
I removed this display function that formats the field data.
$note = forDisplay( fromStorage( $row[2] ) );
After (I removed the "forDisplay" wrapping function):
$note = fromStorage( $row[2] )
I used to php code years ago, so my code may look antiquated (in fact I've never used OOP PHP code!)
The webpage now looks correct using the CuteEditor stored html.