Glad you mentioned East Jerusalem.
Why is UNWRA a problem in East Jerusalem?
Let’s explore why UNWRA are in East Jerusalem.
After the six day war Israel effectively annexed East Jerusalem and its surroundings, applying law and administration to these areas. Among the annexed Palestinian villages was Shuafat refugee camp. As a result, Shuafat’s residents effectively fulfilled their demand of return by becoming residents of Israel.
Now as legal residents of Israel they have the right to settle anywhere they want in the country, including the town they or their ancestors came from. Furthermore, they can apply for citizenship on the grounds of proving their desire “to live at peace with their neighbours” the complete fulfilment of return from the Palestinians own extreme interpretation of Resolution 194.
The refugees who have become residents of Israel have acquired in practice the ability to return. Given this, UNWRA could have announced that it had no more business within the boundaries of Jerusalem and refused to register the refugees in East Jerusalem and their tens of thousands of descendants as refugees.
Yet UNWRA made no such announcement and the inhabitants of Shuafat refugee camp, who for the most part were born after 1948 and after 1967 annexation of Jerusalem, remain registered Palestinian refugees.
So, you can be a refugee when you are a citizen of another country and you can be a refugee when you are a resident of Israel.