Was it Palestine when it was built?
It was JUDEA, a province of Israel when Jesus was born there. Even the Romans called it Judea (from Judah, son of Jacob, and source of the name "Jews" ).
Just because Muslim armies occupied it 1800 years later doesn't make it any less Israel or Jewish land. Muslim armies also invaded and conquered Spain, occupying it for 770 years before it was also liberated. Neither land has any importance in Islam.
At the time it was reconstructed (6th Century), the Byzantines who ruled the place called it “Palestina Secunda”.