$headers = array("HTML\\1.0","HTML\\1.1");
$pattern = '/HTML\\\1\.[01]/';
$newHeaders = preg_replace($pattern, "", $headers);
You have to escape the backslash in the subject and then use three backslashes in the pattern.
You have to use a backslash before the period to escape it in the pattern, otherwise the period is treated as a special character, without the backslash it means any single character. The brackets around 0 and 1 mean either character will be matched.
You could also add the start identifier ^ and end identifier $ to the pattern $pattern = '/^HTML\\\1\.[01]$/';
Without these the pattern the above will match strings like HTML\1.123456