The quotation in question is “The Arabs will have to go, but one needs an opportune moment for making it happen, such as war.”
With regard to the first part of the quotation, “The Arabs will have to go,” this piece makes a strong case that he, at best, relied on a mistranslation of the Hebrew by others rather than going back to the original source (the mistranslation saying the exact opposite of the original writing’s “We do not want and do not need to expel Arabs and take their places”).
With regard to the rest of the quote, the ethics committee at Pappe’s University of Exeter determined that this was a “fair and accurate paraphrase” of sources relied upon by Pappe (without specifying the sources), but was mistakenly put in quotes.
This raises the obvious question of how this could be a fair and accurate paraphrase if the first part of the quotation was incorrect. On that point, the ethics committee apparently concluded that the fact that others incorrectly “translated” the first part of the quotation even more egregiously exonerates Pappe.
I wasn’t aware of this controversy previously, and I haven’t gone back to the original Hebrew sources. But if the linked-to piece is correct, it looks like Pappe took a bogus English translation of a Ben-Gurion quote that had been repeated by others, then “paraphrased” some other material that he nevertheless put into quotation marks, and combined them into a quotation falsely suggesting that Ben-Gurion had a longstanding to expel the Arabs of Palestine.
In fairness to Pappe, in the editing process things like this can happen inadvertently, and can especially happen if the mistake creates a quotation that seems perfectly sensible to the author based on his ideology–one is much less likely to carefully check a quotation that “sounds right” than one that doesn’t. But it certainly doesn’t help Pappe’s case that he attributes the difficulty this has caused him not to his own errors, but to the machinations of “Zionist hooligans,” [UPDATE: fwiw, an old Soviet propaganda term used to denounce American Soviet Jewry activists as well as Israelis] which hardly makes him sound like an objective scholar pursuing the truth.