I wondered about this too, as we sometimes fly into ABQ to visit family, and I'm a big TWA fan. (Dad worked for TWA for over 30 years in SFO, and I maintain twahistory.com, where I'm posting a lot of the stuff I've collected.)
The C gates were a smaller concourse, I understand. From this thread on airliners.net:
http://tinyurl.com/ylos94g
..which talks about the C concourse, which was just TWA.
Here's a snippet:
Once upon a time, there used to be a C Concourse at the Sunport, with three jetways (C1-C3). It was accessed via an escalator to the right of the ticketing counters. TWA used all three of these gates up until the early to mid 90s.
When TWA reduced flights to ABQ and moved to the B Concourse, these gates lay dormant for a long time and eventually the jetways were removed but the concourse remained. I can't remember exactly when it occurred, but the entire concourse has been removed. The current aerial imagery in Google Earth shows the concourse intact (without jetways) while Bing Maps shows the current state where the building now ends with the Sunport Police offices.
Hope it helps!