While I don't recommend messing with the layout, if you absolutely can't live with having that transaction information readily available to you, you can relocate this part of the code to somewhere else in the file. /admin/orders.php
Code:
if ($order->info['payment_module_code']) {
if (file_exists(DIR_FS_CATALOG_MODULES . 'payment/' . $order->info['payment_module_code'] . '.php')) {
require(DIR_FS_CATALOG_MODULES . 'payment/' . $order->info['payment_module_code'] . '.php');
require(DIR_FS_CATALOG_LANGUAGES . $_SESSION['language'] . '/modules/payment/' . $order->info['payment_module_code'] . '.php');
$module = new $order->info['payment_module_code'];
// echo $module->admin_notification($oID);
}
}