Ok your phone doesn't support the MT memory location so use the ME. Also your phone does't support the command AT^SMGR=1 fine use AT+SMGR=1.

Still you need to clean all the memory ME from all the sms present, and your pic micro should enquire the modem and check if a sms is present. If one sms is present then your pic program will decode it and takes the appropriate action, at the end, before returning to the main routine, the pic program must DELETE the sms so that the phone memory ME returns to be clean again. To do that your pic program will send the following command : AT+CMGD=1

Al.