For this claim, there appears to be extremely little by way of actual evidence. In deed, it seems only the claims of Ion Mihai Pacepa in the linked essay, and an interview, are ever referenced as sources for this claim.
In the interview, Pacepa actually admits he was not even directly involved in the alleged events, but states that he was told of this by Aleksandr Sakharovsky (now deceased) years back.
I was not involved in the creation of Liberation Theology per se. From Sakharovsky I learned, however, that in 1968 the KGB-created Christian Peace Conference, supported by the world-wide World Peace Council, was able to manoeuvre a group of leftist South American bishops into holding a Conference of Latin American Bishops at Medellin, Colombia. The Conference’s official task was to ameliorate poverty. Its undeclared goal was to recognise a new religious movement encouraging the poor to rebel against the ‘institutionalised violence of poverty’, and to recommend the new movement to the World Council of Churches for official approval.
Basically, this leaves us with a single person alleging a second-hand claim, without any known documents or living people involved to back it up.
Though the evidence for this already seems weak, there are some who have refuted it further.
The Wikipedia page cites an article by Damian Thompson, pointing out some ambiguity.
Communist era general of Romania's secret police, Ion Mihai Pacepa, claims that KGB created liberation theology. According to Damian Thompson this is not certain even though liberation theology is a quasi-Marxist movement and advantageous to Moscow, as it did not condemn even Brezhnev era atrocities.
An article on Crux also suggests that Pacepa is perhaps overstating the possible amount of KGB involvement, if there was any. It also cites one scholar as stating these claims are just a "conspiracy theory".
Most experts on Latin American religion believe the forces underlying both liberation theology and the expansion of Evangelical and Pentecostal Christianity were largely home-grown. Samuel Escobar, a Peru-based Protestant scholar on missionary work, calls claims that Latin America’s religious trends are a result of foreign influence a “conspiracy theory.”
There is also a very blunt post on Huffington Post by Kerry Walters challenging Pacepa's credibility.
Pacepa defected in 1978 and has been feeding conspiracy stories to the U.S. ever since, including the claim that the KGB, the Soviet intelligence apparatus, masterminded the 1963 assassination of President Kennedy.
This article goes on to point out discrepancies in the alleged timeline of events.
Liberation theology arose in the mid-1950s—before the supposed KGB program began—when priests in rightwing Latin American countries began preaching that the Church had a holy obligation to work for social and economic justice. They pointed out that the Jesus of the gospels privileged the poor and the downtrodden, and argued that the Church should do likewise.
They do concede this may have been something the KGB may have attempted in some way, but that it would be disingenuous to call the result the work of the KGB.
Did the KGB hope to manipulate priests, prelates, and laypersons who already embraced liberation theology? Probably. But this is a far cry from Pacepa’s claim that defenders of it were either willing pawns or unwitting dupes of a scheme cooked up in Moscow. Their embrace of the biblical values of love, compassion, nonviolence, and prayer were incompatible with Marx’s call for class warfare, much less Soviet totalitarianism.
It concludes that the main reason this claim is being propagated at all is because of ulterior agendas rather than a basis in hard evidence. Agendas such as discrediting Pope Francis, President Obama, or anyone else who happens to have some connect are some possible reasons I've seen suggested.
