At the time when the Jews were not allowed to leave Russia, there were demonstrations all over the world against the Russian government.
The Rebbe was against these demonstrations, one of the reasons the Rebbe gave was the damage they were doing to the Yidden in Russia.
An excerpt from a letter of the Rebbe:
"…The wisdom of the said approach is borne out also by the experience in regard to helping Jews behind the Iron Curtain. There are those who claim that anti-Soviet demonstrations and similar actions will induce the Kremlin to change its policy. Others, myself included, are convinced that "quiet diplomacy" has been effective, and certainly not counter-productive. I urged and pleaded - behind the scenes, of course for such an approach by Jewish leaders. Unfortunately, my pleadings were unheeded."
View the full letter here: chabad.org/4454265
During Kos Shel Brocho on Acharon Shel Pesach 5730, a person approached the Rebbe and wanted the Rebbe to sign that he is in favor of the demonstrations (for the Jews leaving Russia). And the Rebbe responded more or less with these words:
"Because of the demonstrations, a few families are leaving Russia, and if not for the demonstrations I know the names of thousands that would have left Russia!"
As the aforementioned began to leave, the Rebbe turned to Mr. Kalman, who was standing nearby, and asked him if he knew him. He answered the question in the affirmative. The Rebbe said to him:
"See to it that he stops the demonstrations… etc."
The Rebbe once said that one should not listen to the Jews in Russia who demanded that the demonstrations continue. Similar to someone who is sick, one listens only to the doctor, not to the patient who has no idea about medicine.
Before us are questions that Rabbi Yehuda Leib Groner asked the Rebbe, and the Rebbe's answer.
Listen to the audio of 11 Shevat 5731:
The tremendous trouble that the demonstrations caused in USSR
For a comprehensive view and collection see the sefer דיעדושקא - הרבי מליובאוויטש ויהדות רוסיה