T F stands for "Totally Fucked" -- Pre 1970's expression that is abbreviation for a slang that could not be uttered, due to social restrictions of the time. Fuck and all its conjugations were not the common slang of pre 1970's American campuses. The word Fuck was still taboo, until later in US history, after celebrities and politicians began saying it in public.
The significance is that to say the expression TF as "Totally Fucked" was a final epithet for the situation that warranted the oath. There was at the time no lower epithet to describe your sisters' promiscuity, or the arrest record of your best friend who is now in a coma from OD of LSD.
It is similar to older yeoman remarks like: SNAFU- "systems normal all fucked up"; SOA- "Standard Operating Procedure"... and the like.
Some significance to the importance of the loss of this expression is in the written record back in the 70's of the Nixon Tapes from his Watergate SNAFU... when "expletive deleted" was bleeped out, and bracketed in the periodicals. Most readers filled in the blanks with a T F or equivalent.
Then of course Geo Carlin rambled into history as he spoke of the words one cannot utter on TV, or was that Lenny Bruce?
After we began laughing at comedians and politicians for making fuck and all its forms expletives, T F lost its valuable place depicting the lowest of conditions. >>pd
"That's T F," said LBJ to RFK right after JFK was shot dead.