On 10th July, 1943, the British taped a conversation between General Georg Neuffer and General Gerhard Bassenge in which the former asked:
What will they say when they find our graves in Poland? The [Soviet] OGPU couldn't have done any worse. I myself saw a train in LUDOWICE? near Minsk. I must say straight away that it was revolting, a horrible sight. There were trucks full of men, women and children - really small children. That is really a shock, this sight. The women, the small children, who were naturally unaware of what was happening. Naturally I didn't watch how they were murdered. There were German policemen with machine pistols all around, and you know who they had with them? Lithuanians, or something like that, in brown uniforms, who did it.
Stephen Tyas here believes that this may refer to an incident whereby, as recounted by Breitman here, a Lithuanian Schutzmannschaft battalion shot 1,300 civilians in the township of Smilovichi on 14 October, 1941. Tyas, p.7, adds two sentence from the transcript that Burleigh omits:
The German Jews were also sent to the Minsk district, and they were gradually killed off, so far as they survived the other treatment. By treatment I mean housing and food and so on.Tyas then cites a Luftwaffe radio operator called Jochen, overheard on 27.8.43, who claimed to have seen 8,500 German Jews being shot in Minsk.
A second conversation printed by Sönke Neitzel was that between Colonels Reimann and Koehnke recorded on December 19th, 1943, in which Reimann stated that a senior police officer had told him about the shooting of thousands of Jewish women and children in Berdichev and Zhitomir.
These conversations are just one form of evidence concerning German wartime knowledge of shootings. Other sources include diaries and letters home from the troops. For example, Burleigh, p.437, has extracts from the diary of Karl Dürkefälden. In Spring 1942, Dürkefälden noted that his brother-in-law, who was working in the Ukraine, had told him he'd seen mass shootings by police units: "There are no more Jews in the Ukraine, whoever didn't escape was shot," Dürkefälden concluded. A few days after writing this, Dürkefälden was told by some soldiers about the mass murder of Jews in Poland, shot "in their thousands." And Dürkefälden later heard from his stepmother, who was working in a local hospital, that she'd learned from wounded soldiers there that "We have bumped off ten thousand Jews in Russia." Finally, Dürkefälden learned of the murder of the Jews of Kiev, and the shooting and gassing of French Jews in Poland, from a soldier on leave from Vilna.
Many other such examples are given by Evans here. For example, the diplomat Ulrich von Hassell wrote in his dairy on 15.5.43:
Shocking reports come in from the good [Max] Fraunendorfer [administrator in the General Government] in Poland. While [Hans] Frank publicly declares he wanted to give Poland a dignified and free existence, and while the gang tries in vain to befuddle world opinion about [better 'with'] the Katyn murders, the SS in Poland carries on most shamefully. Countless Jews have been gassed in specially built chambers, at least 100,000. [...] Meanwhile the unhappy remnants of the Jews [in Warsaw] prepared to defend themselves, and there is heavy fighting which will certainly lead to their complete extermination by the SS.In conclusion, therefore, by mid-1943, the Nazis' extermination of the Jews was known to many Germans in the military and in civilian life.