Honestly. I don't think there is anything the Israeli Government can do to repair the damage in Israel-Turkey relations. Turkey's a Muslim country, and they just don't like us Jews. Simple as that. They may like our money, but there's potentially lots more from Arab countries.
Sometimes people have to reach rock bottom to make crucial decisions. That's what happened when the State of Israel was declared. The Labor Zionist leaders, like David Ben-Gurion's group were disillusioned believing that Britain and other countries would support a Jewish state, even though facts showed otherwise. Only after desperate Jewish refugees, survivors of the Nazi Holocaust were refused entry to the HolyLand by the British and it became more and more obvious that the British supported the Arabs, did the Zionists declare the establishment of the State of Israel.
Many Israelis still quest foreign support and approval. It's dangerous and pathetic.
During this visit to the states, I had some interesting conversations in stores etc with ordinary Americans. They all professed pro-Israel views, wondering why their government and the media are so anti-Israel. "Why is everyone always criticizing Israel?" That was a common refrain.
The State of Israel must face the truth. Nothing we do will make other governments love us, support us etc. Our policies must be what's best for us, and then at least we'll get some respect. It starts with self-respect.