Current, and as far as I know, older Finnish history treats the Allied offers for aid as one of the Great Power strategems during the early stage of the Second World War. Almost every time the Allied offers for help are discussed, it is also mentioned that the "real" objective was the seizure of Swedish iron ore fields. However, this is not exactly new knowledge: even during the war, informed people in the Finnish (and Swedish) governments were perfectly able to guess the same thing. This is also, as far as I know, the key reason why the Swedes did not give the Allies the permission to move their troops through northern Sweden.

That said, the failure of the Western aid did shock quite a few people in Finland. Before the war, the Finnish security policy was to a large extent predicated on the League of Nations and the belief that either Germany or Western powers would come to Finland's aid if the worst came to worst. This may even have been a reasonable assessment until about 1938, after which Finland's geopolitical situation worsened very rapidly - quite possibly so rapidly that most politicians did not really understand the extent to which the balance of power had shifted in the Baltic region. Not only many (though by no means all) politicians but great numbers of ordinary Finns believed that Finland, as an "outpost of the West", would receive military aid; when that did not happen, the resulting resentment from being abandoned by the Western Allies was almost certainly a factor that in 1941 helped Finns to accept a bargain with the "devil farther away" - Hitler.

Post-war, the proof that the bulk of the Allied expeditionary force would've stayed in northern Sweden became one of the primary lessons of geopolitics taught to Finnish soldiers and politicians. The episode served, and still serves, as a reminder to Finns: that Great Powers do not care and that even if they promise to help Finland in the future, "it won't be because of our blue eyes" but because helping Finland promotes their strategic interests.