You're sending "$AVREQ,911DEMO01,1*CHKSUM" from Terminal
and it shows "$AVREQ,911DEMO01,1*5B" in the SMS proxy window.
That is bacause GpsGate removes your checksum (*CHKSUM) and add one itself.
If you calculate the checksun of "AVREQ,911DEMO01,1" you'll get 5B.
You can use this page to calculate it: http://www.hhhh.org/wiml/proj/nmeaxor.html
Try sending "$AVREQ,911DEMO01,1*5B" and "$AVREQ,911DEMO01,1". You'll get same result in SMS Proxy window.
Note that the answer in your case ($AVRSP,911DEMO1,02*4F) means "Wrong password"
Hope it helps you.