Well before the work began Israel told and received approval from the Islamic Waqf and the Jordanian government. The Muslim outrage is 100% manufactured in order to score propaganda points with those who are easily swayed.
There's the problem right there - the government of the only Jewish state on Earth asking the permission of someone other than rabbis to do something on or near to Temple Mount. It is like the US asking North Korea for permission to build a by-pass road around the Washington Monument. My solution is in Post #38.