East Jerusalem is under Israeli jurisdiction and has been for a long time. Perhaps a deal will be made for two-state solution in the future where that changes but that’s the situation at the moment.
As for Al-Aqsa mosque.. putting aside Islam, Christianity and Judaism alike are built on myths…. MEMO itself argued converting Ayia Sophia into a Mosque was Turkish and Muslim right. Principles require… wait for it…. following an actual principle. If converting Ayia Sophia to a Mosque is fine for Muslims, you can’t come back later and claim the same is not true for Al-Aqsa. Figure out what your actual morals are . Then get back to the rest of us.