In Exchange EWS when trying to delete an item you get the following error : cannot find an overload for “delete” and the argument count 0 using
$item.Delete()
You need to give it a an enumeration e.g.
They can be found here : http://msdn.microsoft.com/en-us/library/microsoft.exchange.webservices.data.deletemode(v=exchg.80).aspx
$item.Delete([Microsoft.Exchange.WebServices.Data.DeleteMode]::HardDelete)