Your question is fundamentally flawed. There was no Palestinian government per se during WW2. After WW1 and the dissolution of the Ottoman Empire, the British gained control of the area via the Palestinian Mandate. The British established a Mandatory Government, which was led by British High Commissioner, and was in essence a colonial government.

The Palestinian Mandate required the British to establish some type of self rule in Palestine, but the majority Arab population refused to participate in any government in which Jews were allowed to participate. Due to this, Palestine did not have its own government in the interwar years, or during WW2.

So the answer to your question is no. The Palestinian Government did not provide aid to Jewish refugees, nor did they have an opinion on the final solution. Because the entity you're speaking of didn't exist.

majority Arab population refused to participate in any government in which Jews were allowed to participate.

It was more a question of formally accepting the Mandate and requesting more members in the Council, (the British wanted 10 appointed members, 10 Arab and 2 Jews), than vetoing Jewish participation.

Technically Palestine did have it's own goverment/nationality albeit only nominally and actually was administrated by the British as correctly noted. Continuing on the same pattern one could argue that the Palestinian government maintained the provisions of the White Bible prohibiting Jewish immigration of Jews fleeing from the Holocaust. On the other hand the Jewish efforts of sending commandos to aid Jews, like Hannah Szenez to Hungary or Simon Peres' father to Greece, were under the guise of the Palestinian participation of the war effort. Same goes for direct Jewish aid of the Yishuv to Resistance groups in Europe in exchange of helping Jews in their respective countries. On the other hand Palestine regiments were raised during WW2 and first participated in the Battle of Greece as part of the British expeditionary force. They were captured by the Germans and a big part of the Arab conscripts defected and joined the 13th Muslim Mountain Division of the SS.

So while I also probably suspect that the OP intended Palestinian as the term is currently understood, (Arab), technically the response of the Palestinian goverment was to participate in the war effort with no particurlar regard to the mass murder of Jews in Europe and actually actively working against providing a rescue haven, (as per Struma tragedy).