Saying God does not listen to the prayers of non-jws goes against all the little stories in the WT publications where non-jws are praying to God for help and jws drop by shortly after that.
*** Bible Teach book bt chap. 7 p. 59 par. 17 Declaring “the Good News About Jesus” *** (first used in 1995, then 2001, and again, same one)
As evidence that this is taking place, some of those whom we approach in our ministry say that they had been praying for spiritual guidance. Consider one experience in which two Kingdom publishers were accompanied by a small child. At the end of the morning, the two Witnesses were about to stop their preaching work, but the child was unusually eager to go to the next home. In fact, he went by himself and knocked on the door! When a young lady opened the door, the two adult Witnesses approached to talk to her. To their surprise, the woman explained that she had just been praying for someone to call on her to help her understand the Bible. A Bible study was arranged!
*** jv chap. 24 p. 550 By Human Power? Or by God’s Spirit? ***
On countless occasions, as they have shared in their ministry, they have seen convincing evidence of heavenly direction. For example, in Rio de Janeiro, Brazil, a group of Witnesses were completing their house-to-house calls one Sunday when one of the group said: “I want to continue working a while. For some reason I want to go to that house.” The one in charge of the group suggested that they leave it for another day, but the publisher insisted. At that door the Witness found a woman who, with tears streaming down her face, said that she had just been praying for help. She had previously been contacted by the Witnesses but had not shown interest in the Bible’s message. However, the sudden death of her husband had made her realize her need for spiritual help. She had looked for the Kingdom Hall, but in vain. Earnestly she had been praying to God for help, and now it was at her door. Not long thereafter she was baptized. She was convinced that God had heard her prayer and had taken the needed action to provide an answer.—Ps. 65:2.
*** w79 7/15 p. 15 par. 6 Preaching in a Lawless World ***
This separating work has indeed been carried forward under angelic direction. (Matt. 25:31, 32) And in conjunction with it there has been angelic aid in declaring the “good news,” for how often it has happened that a sincere person has prayed to God for help, only to find one of Jehovah’s Witnesses standing at his door!
*** w63 8/15 p. 510 Her Prayer Answered ***
One of Jehovah’s witnesses in Massachusetts (U.S.A.) had this experience: “I called at the door the other day and as I started to witness the smiling lady said: ‘Are you one of Jehovah’s witnesses?’ I assented. She then asked me in and told me she had just been praying that one would call. And as soon as she had prayed the doorbell rang, and I was there. The significant part of that call was that I did not intend to call at that house when I got out of my car. I had previously left two magazines with a man who showed very little interest, but then suddenly the thought came to me to call there anyway.”