I think you have answered your own question: the United States did not retaliate for the bombing of the U.S. Marine Barracks in Beirut on October 23, 1983, which caused the death of 241 Americans (all military personnel). There were two main obstacles to retaliation: it was not clear at the time against whom such retaliation should be directed and attack helped convince the American leadership that the mission in Beirut needed to be terminated.

Even before the attack, the Marines’ mission was controversial and growing unpopular. The Marines were there as part of the Multi National Force (consisting primarily of American, French, and Italian troops, with a token British participation) deployed in August 1982. The MNF’s initial mission was to allow the Palestine Liberation Organization to escape from Beirut by forming a buffer zone between the Israeli Army (which had invaded Lebanon in June 1982) and the PLO. This was felt preferable to the possibility of house-to-house fighting in Beirut between Israel and the PLO, which would have devasted the civilian community, destroyed the government of Lebanon, drawn other factions into the conflict, and possibly sparked a larger regional war. After this mission was accomplished, the MNF was mostly withdrawn, then sent back after the assassination of Lebanese President Bashir Gemayel and remained to support the Lebanese government and train the Lebanese Armed Forces (ostensibly the official national army but in practical terms one of many militias). The MNF was allowed to defend itself and retaliate against attacks but didn't have an explicit mission of pacifying or controlling territory.

By early 1983, there was substantial division in Congress and the Reagan Administration over continued participation in the MNF. On April 18, 1983, the U.S. embassy in Beirut was hit by a suicide truck bomb, killing 63 people total, of whom 17 were Americans, including 8 CIA agents who happened to be attending a meeting at the embassy. Nonetheless, U.S. Secretary of State George Shultz wanted continued engagement. In April and May, he had negotiated a ceasefire between Israel and Lebanon, the May 15 Agreement, which paved the way for Israel to withdraw. In the short term, this agreement intensified fighting as other factions prepared to occupy the territory Israel would be vacating. The MNF’s attempts at quelling such violence were ineffective, while its association with the LAF made other factions perceive the MNF as an ally of that faction rather than a neutral force. By this time, U.S. Secretary of Defense Caspar Weinberger believed the MNF no longer had any achievable mission in Beirut and should therefore be removed. After the embassy bombing, Weinberger became convinced it was only a matter of time until a similar attack was made against the Marines.

The Beirut barracks attacks of October 23, 1983 were claimed by Islamic Jihad, which had also claimed the April embassy bombing. There were actually two attacks: just minutes after the American barracks was hit, a very similar attack was carried out against a French barracks, killing 58 French servicemembers (all paratroopers). Who was Islamic Jihad? Nowadays the most commonly encountered view, to the point of universality is that Islamic Jihad was a name used by Hezbollah in its early days. Hezbollah is of course a militant Shi'ite organization in Lebanon that was, at that time, to a great extent funded and directed by Iran's government and Revolutionary Guard Corps. In 2003, an American court actually held Iran liable for the attacks. To some extent the controversy over Islamic Jihad’s identity has been written out of history and many 21st century authors simply say that the Beirut attacks and similar acts were carried out by Hezbollah, which used to be called Islamic Jihad. But there was not such a consensus in October 1983: back then the mainstream media was reporting that Islamic Jihad's identify was mysterious. Maybe it had ties to Iran but maybe it did not. Also, Islamic Jihad (and other organizations) tended to claim credit for anything that happened, so maybe there was another culprit. Maybe, some argued at the time, Islamic Jihad did not even exist in any real sense, and was somewhere between a name used by prank callers and a decentralized movement with no real organization or members. We have better documentation now, though.

Finding an enemy was difficult because the Lebanese Civil War and expanding regional crisis were multilateral affairs. During their mission in Beirut which had begun in August 1982, the Marines' main combat actions had been against two other factions: the Druze-dominated Progressive Socialist Party led by Walid Jumblatt and Amal, a Shi'ite militia. Both the Druze and Amal were largely backed by Syria at this time. There was also tension with the Syrian Army, which had a substantial presence in Lebanon since 1976. Retaliating against the wrong faction might be extremely counterproductive. And escalating conflict with Iran was not to be undertaken lightly. I'll also note that as the Iran-Hezbollah-Lebanon connection became clearer through the hostage-taking campaign of the mid-80s, the Reagan Administration's response was actually to deal covertly with Iran, not to launch violent retaliations.

The French government, at this time headed by Socialist president Francois Mitterand, was not so hesitant and on November 18, 1983 went forward with an airstrike on a former LAF barracks in Baalbek occupied by Shi’ite militants and trainers from the Iranian Revolutionary Guard Corps. The United States had initially been part of the planning of this attack but dropped out on or about November 16, winding up all retaliation plans on or about November 22. Mitterand was incensed that the Americans had left France to go it alone. A recent article suggests Weinberger made the relevant decisions unilaterally without Reagan’s approval. The article suggests Weinberger and the Defense Department wanted to maintain good relations with Persian Gulf states for reasons of Cold War geopolitics.

So ultimately the United States did not directly retaliate for the attack on its barracks in Beirut. Subsequent strikes targeted Druze and Syrian positions, including the massive shore bombardment by the battleship USS New Jersey on February 8, 1984. But this was a parting shot in every sense of the word: The last Marines of the MNF had left Lebanon the previous day.