As one would expect, with mixed feelings. Even before the war, the officer corps of the Finnish army was, on average, favorably disposed towards the Germans, although they were far more ambivalent about the Nazi regime (this stemmed from the fact that Finnish military drew a majority of its pre-war higher officer corps and many of its traditions from the First World War Imperial German Jaeger Battalion 27, which was composed of Finnish volunteers who wanted to receive military training in order to liberate Finland). Added to this historical disposition were of course the recent experiences, and as a result, the initial phase of the Lapland War was in actuality a war only in name. On 11 September 1944, the Finnish and the German army secretly agreed that the Germans would pull out from northern Finland peacefully, and Finnish troops would then occupy the abandoned positions, but that both sides would act as if they were actually fighting each other and so the Finns would seem to comply with the armistice terms, which included engaging the Germans no later than 15th September.

From what I've read, quite a few officers considered the ultimate order to engage the Germans as more or less dishonorable betrayal - although the decision was helped by the Germans, who on 15th September attempted a surprise invasion of strategically placed Suursaari island on the Gulf of Finland. The invasion was repulsed with heavy German losses, and it provided a propaganda coup for the Finnish government against remaining pro-German sentiment in the military and the populace.

In the end, needs must when the Devil drives, and in this case the devil was truly riding the Finns: on 30th September, the Allied Control Commission, that is, the Soviets through LTGEN Savonenkov, informed the Finnish political leadership in no uncertain terms that if the Finnish military does not want or cannot engage the retreating Germans in Lapland, the Red Army will be more than happy to lend a hand. Even before these and other overt Soviet threats, Mannerheim had appointed a hero of Winter War (and no friend of the Germans), LTGEN Siilassvuo, as commander of the Finnish military in Northern Finland. Siilasvuo took command as scheduled on 27th September, and as his first act, ordered all communications with the Germans severed. The next morning, advancing Finnish troops encountered German rearguard in position about 20 km west of the village of Pudasjärvi; after the Germans refused a demand to surrender, the Finnish troops opened fire.

Even though the officer corps were somewhat favorably disposed towards the Germans, the fighting men cared less. In any case, most of the troops in the Lapland War were fresh conscripts straight out from basic training, because the terms of the armistice required the Finns to greatly reduce the size of the army, because the older troops had had enough of the fighting in general, and - to some extent - because there were suspicions that older troops may not be very motivated to fight Germans in particular. The attitude of the military hardened, however, as the Germans began to systematically destroy the infrastructure and booby-trap the remains according to their scorched earth policy, particularly because many troops were locals who were appalled by this destruction of their homelands. In the end, the German scorched earth policy undid what ties remained between the Finns and the Germans, to the extent that even today, people in Lapland joke about checking German tourists for matches or lighters.