How was the Holocaust taught behind the Iron Curtain? What state were the death camps kept in? Did people visit touristically? What were they taught?

Stalinist anti-semitism became particularly clear after the war. When Israel became an independent state Stalin's concern grew that it would turn into an American satellite. With the air drops in West Berlin and eventually the Korean war, Stalin found that his former ally in the west had become a significant threat.

The mass killing of Jews was severely downplayed in the Soviet Union. Stalin portrayed Soviets as the main victims of Nazi aggression, and in the Soviet narrative the war really began when Hitler betrayed Stalin and invaded the Soviet Union by crossing the Molotov-Ribbentrop line in 1941 (Rather than in 1939 when Hitler and Stalin jointly invaded eastern Europe). Stalin counted many of those killed in Eastern Poland and the former Baltic States as Soviet victims, even though they had only been under his control for two years before the Nazi invasion (and had suffered greatly under communist rule, for example the execution of more than 20,000 Polish officers at Katyn, Poland).

After the war, Stalin saw support for Zionism growing within the Soviet Union. Many people during the war had also seen parts of the west, and he could no longer keep up the illusion that life was objectively better under his rule. He claimed that many Jews were acting as American spies and needed to be rooted out. There was a specific campaign against Jewish doctors, and Stalin's own doctor was arrested after he suggested that Stalin should end his political career in his old age (he was 72 years old in 1950). Show trials were put on in Moscow in which Jewish prisoners confessed to a litany of crimes after they had endured torture. It is possible that if Stalin had not died in 1953 then a more systematic killing campaign against Jews may have been organized (like those that had taken place mostly against Poles and Ukrainians during the Great Terror of 1937-1938).

Something important to note is that after the war, the American and British understanding of the Holocaust was also skewed. American soldiers took pictures at the liberation of concentration camps like Dachau and thought they had seen the worst of Nazi crimes. This was far from the truth since the British and Americans did not find a single Nazi death camp (such as Chelmno, Sobibor, Belzec, Majdanek, Treblinka, or Auschwitz-Birkenau). Additionally, nearly all of the mass shooting sites (such as Babi Yar near Kiev) were on the eastern side of the former Molotov-Ribbentrop line. The sites of all of these atrocities fell behind the Iron Curtain and wouldn't be fully accessible to Western historians until after the fall of the Soviet Union.

Source: Timothy Snyder, Bloodlands, Basic Books (2010).