$re = '/(<\s*(\w+)[^<]*?)\s+this-html=[\'"]([^"\']*)[\'"]([^>]*?)\s*>[\w\W]*?(<\/\2>)/m';
$str = '<div this-html="text goes here!" class="something">test</div><div this-html="another test">Option is visible on preview/publish</div>';
$subst = "$1$4>$3$5";
$result = preg_replace($re, $subst, $str);
echo "The result of the substitution is ".$result;
Please keep in mind that these code samples are automatically generated and are not guaranteed to work. If you find any syntax errors, feel free to submit a bug report. For a full regex reference for PHP, please visit: http://php.net/manual/en/ref.pcre.php