Most people have never heard of the village of Ghajar (غجر) - no real reason why they should. It has a population of about 2000 Arabs, mostly of the 'Alawi sect of Islam, the same small sect of the current and past presidents of Syria.
The village sits astride the border between Lebanon and Israeli-occupied territory. Whether the Israeli-occupied territory is part of Lebanon or Syria is a point of contention between Israel, Syria and Lebanon. In this regard, Ghajar is similar to another series of villages in this same area, these being the Shaba' Farms.
As shown on the above map, the village is divided in two by the international border. The northern portion of the village is in Lebanon and the southern portion is in Syria, but occupied by Israeli troops since the Six Day War in 1967. During Israel's invasion of southern Lebanon in 1982, Israeli forces occupied the northern portion of Ghajar as well.
When Israel withdrew from Lebanon in 2000, the United Nations delineated the border, again dividing the town between Lebanon and Israeli-occupied Syria. Lebanese forces nominally took control, but in reality, the Lebanese portion became an important base of operations for Hizballah.
According to the Ta'if Accords of 1989 and UN Security Council Resolution 1559 of 2004, all Lebanese militias were supposed to disarm. Israel had withdrawn and there theoretically was no need for Hizballah (or any party) to have an armed resistance wing. Hizballah claimed that Israel had not fully withdrawn from Lebanon, claiming that the Shaba' Farms were actually Lebanese territory, not Syrian. The UN backs Israel on its claim that the Farms are part of Syria. Until Israel withdraws from all of Lebanon - which Hizballah insists includes the Shaba' Farms, Hizballah will maintain the "resistance." This fiction is what I call "Hizballah's Fig Leaf." (See The Shaba' Farms - Hizballah's Fig Leaf.)
During the fighting between Hizballah and Israel in 2006, Israeli troops moved back into the northern section of Ghajar, where they remain today. Israel has committed to withdrawing from the Lebanese side of the border once the security situation warrants it. The new Israeli government said it will wait until after the June 7 elections in Lebanon before determining whether a withdrawal is warranted.
Israel fears that Hizballah will gain more power in the elections. They believe that turning over north Ghajar to the Lebanese is in effect turning it over to Hizballah. Incidentally, the villagers in the northern section prefer to remain under Israeli occupation rather than having to deal with a Hizballah presence again. Economically, they are better off.
Clearly, Israel is occupying a portion of Lebanon. This gives credence to Hizballah's argument that Israel is still in Lebanon, and justification for their continued maintenance of an armed militia. While the Shaba' Farms will still be an issue, an Israeli withdrawal from Ghajar removes one claim Hizballah can make.
Give the northern part back to Lebanon. Force Hizballah to defend maintaining a militia.