I think Joseph is starting to get at the answer to this with his last one-line comment. From what I’ve learned–correct me if I’m wrong–the Gra ruled on when Ashkenazim should defer to minhag hamakom in eretz Yisroel. For example, (again, correct me if I’m wrong) he held that Ashkenazim should not wrap tefillin on chol hamoed in eretz Yisroel as the prevailing minhag hamakom was not to (on account of the Sephardim). In short, I think those following minhag haGra in Israel would have different practices than those following it in the diaspora (can anyone confirm this?).
For the original poster: What specifically were you talking about when you thought of this question? In what cases do you find that Minhag haGra is followed by Ashkenazim in Israel (more so than it would be b’hutz).