It is foolish of Israel to play the legitimacy card when no-one has ever questioned the right of the state of Israel to exist. However, having used the word you can bet people will ask themselves the question:'Well, is Israel legitimate?' And the answer they are likely to come up with is No. Not really. Certainly not morally and possibly not legally. So the only sensible thing for Israel to do is to ensure that it is legitimate by negotiating legitimate borders for itself and then the question is answered once and for all. Few people would question Israel's right to exist like any of the other historically recent colonisers like the US, Canada etc., but they certainly do question its right to maintain an occupation and continued colonisation of Palestine or to create an apartheid State which is what it is seeking to do. Israel's can be legitimate in an instant and removed from the stigma of world pariah by ending the occupation and negotiating final borders for Israel. Simple as that.
Report: Man detained at Newark Airport after entering secure area, prompting evacuation (Haaretz)
from the article: No one is questioning Israel's legitimacy