From my readings it was the Secret Service who told Marina to keep away from the Paines not the FBI. Remember, they were the one in charge of protecting Marina and the children. Maybe FBI agents said so too?
Priscilla McMillan goes over the estrangement in "Marina and Lee." Also Robert Oswald was very upset with the Paines, thought they were dishonest - he believe they lied about not knowing Oswald's rifle was in their garage - and he told Marina his feelings about them, that she shouldn't trust them. Ruth discusses the issue in the very good Mallon book.
And the Walker incident apparently angered Marina. She blamed Ruth for it.
