I watched an FBI Files episode regarding counterterrorism in the 80's, particularly against hijackers of the Lebanese airplane w/ US citizens on it.
And it mentioned how the USA expanded its jurisdiction to fight terrorism around the globe in the 80s.
The show phrased it as sending a message to terrorists that the game has changed and the USA will go across the globe to find you, in order to dissuade any plots of terrorism.
Did this "message" truly cause a downward trend in terrorist attacks?
Up until the 2000s, by far most of the terrorist attacks against US targets, which were mostly in the US, were domestic. If you think of the wave of bombings and assassinations, or attempted assassinations by the KKK, various leftist factions stemming from Communist or psuedo-Communist parties or anarchists from the 1920 Wall Street bombing in NYC to the spate of attacks by The Weather Underground - the FBI's focus was on westerners, not foreigners.
The US did have to deal with terrorism, but often it was tertiary, such as when Americans were caught up in the Palestinian/Israeli conflicts, or when they offered advisors to the Israelis during and after the Munich Olympics attack. Until the attack on Pan Am 103 over Lockerbie, Scotland, the US hadn't really had to send Agents overseas, and terror attacks were predominantly directed against political factions by other domestic factions.