I find this fascinating; I didn't know this functionality existed.
also potentially interesting: is there a no-notification ping? Sometimes I am glad I grew up in the fixed-line era.
> Short Message Type 0 is known as a silent SMS. Any handset must be able to receive such short message irrespective of whether there is memory available in the (U)SIM or ME or not, must acknowledge receipt of the message, but must not indicate its receipt to the user and must discard its contents, so the message will not be stored in the (U)SIM or ME.
However, you can set a validity period, after which undelivered messages are supposed to be deleted. Some carriers here in the U.S., however, don't respect that validity period, so there's really no guarantee.
Other than that, I don't think there is a supported way to delete a message that has been received, unless the text message is sent some other way; maybe other apps, like iMessage, WhatsApp, etc., support this?