PIC TXD -----> (T.IN) MAX232 transmitter (T.OUT) -----> GSM "TXD" connection
PIC RXD <----- (R.OUT) MAX232 receiver (R.IN) <----- GSM "RXD" connection
The GSM modem, being a DCE (data communications equipment) component in the RS-232 conventions, should actually receive its data on the connection marked TXD; this connection is called TXD because it's the data transmitted by the PIC, which is a DTE (data terminal equipment, another RS-232 term), and it's also the data transmitted to the GSM network by the GSM modem.
Conversely, the data received from the GSM network by the modem should be sent out from the GSM modem on the connection marked RXD, and received by the serial port on your PIC board.
It's possible that the designers of the modem did not follow this RS-232 convention, which is very old. In that case, they may have swapped the names of the TXD and RXD signals at the GSM modem.
You can tell which way the modem is connected by just powering it up, and measuring the voltages on the two connections relative to the GND connection. One connection should have around 0V on it; this is the data input to the modem. The other connection should have a negative voltage of at least 3V on it; this is the data output from the modem.
If the negative voltage is present on the connection marked RXD, then the diagram at the top of this post is correct.
If the negative voltage is present on the connection marked TXD, then use this diagram instead:
PIC TXD -----> (T.IN) MAX232 transmitter (T.OUT) -----> GSM "RXD" connection
PIC RXD <----- (R.OUT) MAX232 receiver (R.IN) <----- GSM "TXD" connection
The only difference is that TXD and RXD at the GSM modem are swapped.