This might be a bit late in terms of criticism, but many Finns IOTL and ITTL would argue against presenting the Winter War as the beginning of a dispute over Karelia between Finland and the Soviet Union. Arguably, the better starting point would be 1917-1920, the breakup of the Russian Empire and the creation of an independent Finland. At that time there was the first real effort to create a "Greater Finland" including the areas inhabited by the Finnic Karelians, and that goal was supported by a major proportion of the Finnish population. ITTL, Finland can well argue that when the Russian Empire broke up, the Karelian areas were not the property of the newly created Soviet state, but should have been for ethnic, linguistic and cultural reasons included in an independent Finnish/"pan-Finnic" realm. Then we also have to remember that the ethnic Karelians had been living in these areas for centuries, and their settlement in the area that carries the name of their ethnic group also predated Russian settlement, much of which was comparatively recent.
In the 1920 Treaty of Tartu, Finland received only a small part of its claims in Karelia, which was a big disappointment to many nationalists in Finland, to the extent that some called the treaty "shameful". In the treaty, the Soviet state did affirm the cultural and political rights of the Karelians, and promised to uphold them, as a sort of quid pro quo of the area inhabited by ethnic Karelians not becoming a part of Finland. As is well known, this promise by the Soviet government was soon broken, and what efforts there were to maintain a politically and culturally autonomous Karelia in the 20s and early 30s were squashed in the Stalinist era. The Finns and the Karelians in Soviet Karelia were heavily targeted in Stalin's purges, moreso than the ethnic Russians living in the Karelian areas. In the 30s, many people would come from the USSR to Finland to tell the Finnish authorities and the press about the repression faced by the Finnic people in Soviet Karelia.
So this was the background before the Winter War and the Continuation War, and the Finns would use this background to argue that the Russians have no more right to Karelia than Finland does. Quite obviously the USSR failed to uphold the rights of the indigenous Finnic people in Karelia, and thus for the ethnic Karelians, the Finnish conquest during WWII was a real liberation from Stalinist rule. Due to the history of the Karelians stretching back to the years after WWI and beyond, the issue of Karelia is not only or even predominately tied to the Nazi attack against the USSR, the Finns (and whoever supports them) would argue. The Karelians would need to be considered as having rights as the indigenous population in Karelia (moreso than Russians, even), and their will certainly would not be returning the areas they inhabit to a Russian state.
Now, there would be the fact that the Finns would have expelled the great majority of the ethnic Russian population from the Karelian areas at the end of the war. This is an argument the Russians would use, that returning these areas would be right due to the crime of ethnic cleansing committed by the Finns against Russians, the original inhabitants of the area having to flee from it post-WWII. But then, this is the same argument that could be used today by Germany about East Prussia or by Finland about the Karelian areas Finland lost to the USSR since 1944. The fact on the ground is that these areas have been (IOTL, on one hand, and ITTL, on the other) inhabited be their current populations for several decades. If Finland now demanded its 1920 borders back, Russia would definitely argue about the rights of the Russians living in those Karelian areas, to keep their homes, their communities, and their connection to the Russian state and society. The same would apply to the Finns and Karelians living in Karelia ITTL: giving the Karelian areas to Russia would violate the rights of the people living in Karelia, as they would either have to accept becoming Russian citizens/subjects, or then they would have to leave their homes to become refugees in Finland or elsewhere. The Finns would here argue that many if not most of these people would have roots in Karelia stretching back centuries, as well - something that is not true about the ethnic Russians living in Vyborg or Kaliningrad IOTL. So in that sense the Finnish argument for the rights of the Karelians would be even stronger ITTL than the Russian argument for the ethnic Russians in formerly Finnish Karelia or in the Kaliningrad area IOTL.
So, as you can see, "the Finns conquering the area in league with the Nazis" would be only one side of the argument ITTL, and the Finns could and would level other arguments for keeping Karelia as a part of Finland.