Short version: Super poorly.

A lot of Russo-Polish tension was already present due to a variety of events throughout history (various partitions and the imposition of Russian power in Poland's early history), but the most recent before Katyn being the signing of the Molotov-Ribbentrop Pact in which a treaty of non-aggression was signed between Russia and Germany shortly before the German invasion of Poland in 1939.

The fact that Soviet forces also invaded Poland and then proceeded to kill so many Poles, especially at Katyn, was only rubbing salt into the wound.

For a brief period talk about Katyn was suppressed or sometimes blamed on German soldiers by the Soviets or members of the Party in Poland. This sort of corresponded with a common trend of blaming certain non-German atrocities that had occurred during the war on the Germans, like the massacre at Jedwabne (which was carried out by Poles in the town). In the 1980s as movements like Solidarity rose, Poles began to discuss Katyn more, and in 1985 the Soviet government began to truly come clean about the massacre.

Source: I just wrapped up my undergraduate thesis on Poland form 1945-1989. This is a heavily paraphrased version of an answer and I can point you in the direction of a variety of sources should you choose to research this.