The answer is...outside marching down the Blue Line, not much.
Of course, this is not entirely fair. Their regular reports to the UN show that UNIFIL does do lots of things, mostly to support the Lebanese Armed Forces, although they do nothing to help disarm Hezbollah. Every report includes a paragraph like this:
No progress was achieved with regard to the disarmament of armed groups. Hizbullah continued to acknowledge publicly that it maintained military capabilities. The maintenance of arms outside the control of the State by Hizbullah and other groups in violation of resolution 1701 (2006) continued to restrict the State’s ability to exercise full sovereignty and authority over its territory.One thing I didn't know is that the Trump administration made some efforts to turn UNIFIL into a more useful organization. The Congressional Research Service notes:
U.S. Administrations have disagreed over the mission and size of UNIFIL. Some U.S. officials have described UNIFIL as a stabilizing presence in southern Lebanon, stating that Hezbollah strikes across the Blue Line have significantly decreased since UNSCR 1701 (2006) increased UNIFIL’s troop ceiling from 2,000 to 15,000. A former U.S. Ambassador to Lebanon has noted that “UNIFIL’s value in constraining Hezbollah comes down to its size. Through sheer numbers, it essentially saturates the south. Even if it can evade UNIFIL scrutiny at times, as the tunnels show, Hezbollah does not have the almost complete freedom of movement in the south that it enjoyed under ‘old’UNIFIL.”In contrast, the Trump Administration asserted that UNIFIL “patrols and checkpoints are of plainly limited use when offending parties can simply hide weapons and tunnel entrances on so-called ‘private property.’” The United States and Israel accused Hezbollah of hiding weapons in violation of UNSCR 1701, and pushed for the addition of language to UNIFIL’s mandate that would allow UNIFIL to access and search private property for illicit Hezbollah weapons. Trump Administration officials criticized the government of Lebanon for not facilitating UNIFIL access to key sites, such as the Lebanese origin points of Hezbollah underground tunnels that cross into Israel.In response to U.S. pressure, additional provisions were added to annual resolutions reauthorizing UNIFIL’s mandate. In 2017, U.S. officials successfully advocated for language requiring UNIFIL to notify the Security Council whenever it encountered roadblocks or other obstacles; these incidents are now noted in regular U.N. Secretary General reports on the implementation of UNSCR 1701. In 2019, the Security Council approved U.S.-proposed language calling for the Secretary-General to assess the effectiveness of UNIFIL; the resulting report highlighted several structural weaknesses. In August 2020 the Security Council voted to reauthorize UNIFIL but also reduced UNIFIL’s maximum force strength from 15,000 to 13,000 troops. Then-U.S. Ambassador to the United Nations Kelly Craft stated, “The reduction of the ceiling from 15,000 troops to 13,000 is an important step toward right-sizing a mission that has for years been over-resourced given the limits on its freedom of movement and access.”
The private property issue is serious, and it is not all UNIFIL's fault. The Lebanese Armed Forces do not let UNIFIL enter private roads or property, although it appears that UNIFIL does do some aerial reconnaissance of some private property.
Hezbollah, meanwhile, boasts of over 100,000 missiles, many of them high-precision, and UNIFIL cannot or will not do anything about those.
UNIFIL does have a band, though.
