Read the Wikipedia article I posted with the sources also for perspectives on the political situation. Parts of Iran were seized and controlled by the Russians. They pushed the Polish individuals who were deported to Siberia in 1939 to go to Iran in 1942. When 1946 around the Russians did not leave the parts they seized of Iran and "their" Polish refugees were not forced out. The Kurds who welcomed the refugees openly (in Northern Iran) did not force the Poles to leave when the Soviets eventually pulled out. Also Tehran, which was a mixed city with western influences and already had a sizeable Polish community before the war due to the 1927 Treaty of Friendship, also welcomed Polish refugees. Those that did stay in Iran for the long term, mostly settled in Tehran -- where the mayor & police authorities in 1946 refused any orders to force the Poles out. However the estimates of the number of Poles who remained in Iran beyond 1948 number between 2000 to 4000 -- out of the hundreds of thousands (116,000 from the Soviet Union (6000 of which were Jewish, plus many others from multiple routes) who arrived there.
It should be noted that most of Polish refugees (from by the Soviet Union and other routes) did not stay long in Iraq. Most moved on to other places after a few mere months (including Lebanon, Mandatory Palestine, India, Uganda, Kenya, Tanganyika, Northern and Southern Rhodesia, South Africa, New Zealand and Mexico according to the Wikipedia article you cited). Most of the Polish soldiers from Iran landed up in Italy during the war.
The one point the articles get very correct is that the entire situation was very complex. You had refugees from multiple countries. Both the British and USSR occupying Iran. The food crisis in the Iranian country-side which tended to make refugees unwelcome in rural areas. The major powers seizing and shipping resources out of Iran without compensation (oil, etc.). Effectively no stable central government (i.e. a powerless puppet), and multiple political factions vying for power controlling different parts of the country.