There's not actually much evidence that they cared.
Yes there is, it was the cold war
Soviet spies in America were almost completely absorbed with obtaining information and transmitting that to Russia. Read the entire wikipedia article on known Soviet espionage, and you can see that not a single infiltrator was ever found who targeted a media organization.
Wew lads we wikipedia now
Active measures (Russian: активные мероприятия) is a Soviet term for the actions of political warfare conducted by the Soviet security services (Cheka, OGPU, NKVD, KGB) to influence the course of world events, in addition to collecting intelligence and producing "politically correct" assessment of it. Active measures ranged "from media manipulations to special actions involving various degrees of violence". They were used both abroad and domestically. They included disinformation, propaganda, counterfeiting official documents, assassinations, and political repression, such as penetration into churches, and persecution of political dissidents.
Active measures included the establishment and support of international front organizations (e.g. the World Peace Council); foreign communist, socialist and opposition parties; wars of national liberation in the Third World; and underground, revolutionary, insurgency, criminal, and terrorist groups. The intelligence agencies of Eastern Bloc states also contributed to the program, providing operatives and intelligence for assassinations and other types of covert operations.
Retired KGB Maj. Gen. Oleg Kalugin described active measures as "the heart and soul of Soviet intelligence": "Not intelligence collection, but subversion: active measures to weaken the West, to drive wedges in the Western community alliances of all sorts, particularly NATO, to sow discord among allies, to weaken the United States in the eyes of the people of Europe, Asia, Africa, Latin America, and thus to prepare ground in case the war really occurs."
Active measures was a system of special courses taught in the Andropov Institute of the KGB situated at SVR headquarters in Yasenevo, near Moscow. The head of the "active measures department" was Yuri Modin, former controller of the Cambridge Five spy ring.
For thousands of years generals have sought to control what information their enemies receive and to use information against their enemy's people, the pen is mightier than the sword and generals have been killed by their own side over forged letters for less. The addition of modern institutions capable of deciding the soul of the nation, the academic, religious, political and media, with such speed and ease of infiltration - can you imagine the combined intelligence of the USSR coming together and deciding that being able to influence how their enemies think, believe and process reality for such little cost was not a valuable tool? That to get their enemy to think in a manner useful to them was worthless? Thus, active measures, black propaganda, ideological subversion.
The Soviets just didn't think that kind of thing was very important: they targeted institutions of science and authority directly, because to the Soviet mindset, those were the things that matter. Because they merely ruled by fear in Russia, their own internal demagoguery was actually very under-developed: the looming threat of state violence allowed them to just print official facts without any explanation or arguments to support them, and expect the populace to act like they believe it. No need to actually convince you of anything.
The Soviets did not just target US authority or scientific credibility, that it is common belief that the Soviets did not engage in the same attempts at subversion as the US is probably a sign of how superior the USSR's efforts were. In warfare, especially of the largest war never conducted, one where the fate of the species is at risk - it is clear why the Soviets left no avenue for superiority left unexplored, because to leave the thinking processes, the ideas of the US people alone would be moronic. Likewise the USSR did not merely rule through fear, you can't run society wholly on fear. Use it to terrify dissidents, enforce discipline amongst the more productive yes, but not everyone, they just all become useless with fatigue and you have to consider the people enforcing the fear. Thus state enforced morality, education curriculums, patriotism etc., to supplement the rallying of loyalists against the USA.
Fundamentally, propaganda is about controlling your own population. One example of that is Pravda. If the USSR was really as concerned with changing what Americans think, surely they would have translated Pravda or similar into English? But they didn't do anything like that. The belief that all those foreign forces are conspiring to manipulate American media sounds like propaganda itself to keep people fearful and skeptical of dissenting voices. The reason USSR wasn't interested in affecting the American media, but modern Russia is, is because Russians can read those American media sources now.
Fundamentally propaganda is about promoting a cause. Amongst your people, yes obviously. If I can promote my cause in my enemy, I take away strength from my enemy and add their strength to my own - turning enemies into allies. What general in all the history of mankind has ever rejected such wisdom? Even today, hearts and minds is more important than bullets and mines. Propaganda doesn't need to control, as that is difficult, but enough to influence your opponents into choosing of their own free will to act as you want them to? Treasure trove of soft power unearthed, the kind worth killing for. Propaganda doesn't even need to be factually incorrect lol, just misleading enough.
One example is that of Print media. Of course the USSR was concerned with changing how Americans think, but why the hell would they do it by translating Pravda? That would cost money and the US citizenry would simply reject it for being the mouthpiece of the Soviets. No, you want the information they get to come from their sources, control what information their journalists are allowed to report on or better yet, have their journalists be yours, their teachers be yours, get political momentum going. For allies who are sympathetic to the Soviet cause
there would be translated material ranging from political books, children's literature and so on, ensuring that money and time is not wasted on literature that would merely be burnt.