$re = '/(?!insertedAT\": )\{ \"\$date\": (\"[^\"]*\") \},/i';
$str = '"insertedAt": { "$date": "2018-01-31T11:05:39.447Z" },';
$subst = "\1";
$result = preg_replace($re, $subst, $str, 1);
echo "The result of the substitution is ".$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