Live versions of the song leave out the narrative, letting the music speak for itself. They do sing the "Thela Hun Ginjeet" chorus, though.
The title is an anagram of "Heat in the Jungle." The story is true;
Robert Fripp surreptitiously recorded it while Adrian Belew, breathless, told the rest of the band about something that had just happened to him. Fripp used a similar method to record the dialogue of his song "NYC," which features the sounds of a domestic dispute from the apartment next door to his. It's been reported that for some live versions of "Thela," Belew would tell the story of the NYC argument rather than his own story.
Source: Eric Tamm's excellent Robert Fripp biography: http://www.progressiveears.com/frippbook/contents.htm