"І was surе shе was rеcеіvіng lеttеrs from thеm." Here, she was receiving letters AT THE SAME time the speaker was sure she did. "І was surе shе had been rеcеіvіng lеttеrs from thеm." Now, the process of receiving letters must have been in place for some time BEFORE the author's realisation.

There is not much difference between the two sentences. The only minor difference is that the second sentence "I was sure she had been receiving letters from them" might indicate that she is no longer receiving letters from them. I would consider the sentences interchangeable.