Israel's government is concerned that the U.S. is effectively legitimizing Iran's influence in Lebanon and eroding Israel's freedom of operation there through new understandings reached in Switzerland and the memorandum of understanding signed with Iran last week, two Israeli sources told Axios.Why it matters: Iran has managed to wrap the situation in Lebanon into its negotiations with the U.S. in order to support its proxy, Hezbollah. The Trump administration accepts that it must now contain Israel's actions in Lebanon in order to advance its diplomacy with Iran.Israeli officials worry the new understandings will undermine months of efforts by the U.S. and Israel to weaken Hezbollah and decrease Iran's influence in Lebanon.More immediately, they're also worried about pushback from D.C. each time they want to conduct a strike on Lebanese soil, or pressure from Trump to withdraw from southern Lebanon while the Hezbollah threat still exists.Driving the news: The U.S.-Iran MOU stipulates that both countries and their allies will end all hostilities, including in Lebanon, and ensure the country's territorial integrity and sovereignty — which are undermined by Israel's ongoing occupation in southern Lebanon.There were several rounds of fighting in the days after it was signed, though the latest ceasefire renewal has held since Saturday.Iran threatened to close the Strait of Hormuz and to skip the Switzerland talks if Israel continued its attacks.Once the talks actually began on Sunday, Lebanon was one of the key issues discussed. The parties agreed to create a new "deconfliction cell," together with Lebanon and the Pakistani and Qatari mediators, to ensure the ceasefire holds.Between the lines: Israeli sources claim that new U.S.-Iran agreements on Lebanon erode previous understandings reached between the Netanyahu government and the Biden administration in 2024, which were blessed by the incoming Trump administration.Under the Nov. 2024 Lebanon ceasefire agreement, brokered by the Biden administration, Israel retained the right to act against both imminent threats and emerging threats posed by Hezbollah. Under the current conditions, Israel's freedom of action appears to be limited to imminent threats only.And while the previous ceasefire-monitoring mechanism involved Israel, Lebanon, the U.S., and France, this time Israel is not a direct participant, while Iran is.Furthermore, the Biden-era monitoring mechanism was focused on coordination to dismantle Hezbollah's military infrastructure in southern Lebanon, while this one will focus on de-confliction between the Israeli military and Hezbollah.Behind the scenes: An Israeli source said that while the nuclear elements of the U.S.-Iran deal concerned Prime Minister Benjamin Netanyahu, he is currently much more worried about the Lebanon part.One reason is that Israel's actions against Hezbollah have enormous domestic political salience ahead of October's election."Bibi is hysterical about it," the source said, referring to Netanyahu by his nickname.In recent days, Netanyahu asked his close confidant Ron Dermer, who left government several months ago, to urgently use his relationships within Trump's team to try to influence the U.S.-Iran talks on Lebanon, according to the same Israeli source.The source claimed Dermer's involvement helped lead to a Truth Social post in which Trump threatened to strike Iran if it didn't restrain Hezbollah.A U.S. official confirmed Dermer's participation and said U.S. negotiators in Switzerland spoke to him several times on Sunday to brief him on the Iran talks and get his input. "We were transparent with them," the official said.The other side: Lebanese President Joseph Aoun is willing to accept the new mechanism as long as it is led by the U.S., according to a Lebanese official.Vice President Vance and Trump's envoy Jared Kushner briefed Aoun on the deconfliction mechanism in a call on Monday morning.What they're saying: A senior U.S. official contended that Iran has been deeply involved in Lebanon for decades and claimed Israel doesn't have to be concerned about the new mechanism for Lebanon. "Israel is not out of the mechanism, because the U.S. is in the mechanism. We are so close and coordinated that a direct channel between the U.S. and Iran over Lebanon will only benefit Israel," the U.S. official said.Friction point: "The deconfliction mechanism in Lebanon envisioned by the Trump administration doesn't include Israel and in my view is a major misstep," Sen. Lindsey Graham (R-S.C.), one of Netanyahu's closest allies in Congress, told Axios.On Monday, Netanyahu issued an unusual joint statement with his Defense Minister Israel Katz and Israel Defense Forces chief of staff Gen.