I've neither used "AT+CMGC" nor seen an example of its use.

This command is used to delete or modify some message previously
sumbitted to an SMSC, and as yet undelivered to the addressee.

Provision also seems to be made for other operator-defined
functions on SMSCs, specific to individual carriers/providers.

GSM 07.05 and GSM 03.40 together seem to give us instructions
for its use.  The syntax differs considerably between text-mode
and PDU-mode, but the same data fields are present.  Sections
9.2.2.4, 9.2.3.19 and 9.2.3.20 of GSM 03.40 are especially
important.  The TP-Command-Data field (9.2.3.21) seems to be
used only for the "proprietary" operator-defined functions.

If you have a particular scenario in mind, I'm happy to suggest
a specific command to try.

"AT+CNMA" is used to acknowledge receipt of an SMS (to the
delivering SMSC) when that SMS is routed directly to a devices
serial port (and not stored internally).  This is to ensure
reliable delivery is made, and can happen as a result of a
previous "AT+CNMI" command, or because the SMS originator
specified serial port delivery (a "TE specific" message) in the
DCS message header field.

In text-mode, the acknowledgement command is:

       AT+CNMA

and the PDU-mode equivalent is:

       AT+CNMA=0

(GSM 07.05).

John