The Wikipedia article doesn't really support your view that they emigrate to Israel:
>In 2007, the year Hamas took over Gaza, the Gazan Christian population was at 3,000.[5][33] Israel's subsequent blockade of the territory accelerated the emigration of Christians, with many going to the West Bank, the United States, Canada, or elsewhere in the Arab world.[5]
I think they don't. I think it's as states, that they either emigrate to the West Bank or go far abroad.'
There are extreme efforts in Israel to push Christians out of certain neighbourhoods, for example, in Jerusalem, where people have been going after the Armenians.
Christian population is going down in Palestine, and up in Israel
https://en.wikipedia.org/wiki/Gazan_Christians#Hamas