Their claims are ludicrous once you know that it the land was purchased by Jews in the 1840s, completed in 1872, destroyed by the Jordanians in 1948. The Jerusalem government approved the rebuilding in 2012, but perhaps some new stage in the rebuilding just started.
The Jerusalem Governorate condemned the start of building a new synagogue bearing the name “The Jewel of Israel” located about 200 meters from the blessed Al-Aqsa Mosque from its western side, in the Al-Sharaf neighborhood, considering this measure a new crime against the sanctities and another attempt to Judaize and falsify the Arab face of the city.The Jerusalem Governorate said - in a press statement this evening - that the synagogue is being built on the ruins of an Islamic endowment, warning of the danger of encircling Al-Aqsa Mosque with a series of synagogues and biblical gardens, among which was the "Hurva Synagogue", in an effort to Judaize Al-Aqsa and its surroundings and Jerusalem as a whole in exchange for obliterating every trace. Islamic and Arab in the occupied city and the surrounding Palestinian areas, and added that the occupation deliberately built the Jewish Synagogue west of Al-Aqsa with a huge architectural design so that it distorts its general visual scene and controls it completely, and in order to mimic its domes, and the Church of the Holy Sepulcher in the Old City, knowing that it has built dozens of synagogues and religious Talmudic settlement schools in the Old City with the aim of Judaizing it and expelling the Palestinian Arab population from it.The statement said: "These racist settlement measures [aim to] to prove its entitlement to Jerusalem, through falsification of history, obliteration of facts, distortion of the Islamic urban landscape in the occupied capital, and the creation of a Hebrew model in it.The statement stressed that the city of Jerusalem is Islamic in face, with an Arab identity, and the occupation will not rob it of this fact, no matter how intrusive it is in criminality by all means and methods.
As far as the Arab fear of Jewish buildings dominating the skyline, here is the Jewish Quarter before 1948, with both the Hurva and Tiferet Yisrael domes clearly visible.