Acts 20:22 KJV
And now, behold, I go bound in the spirit unto Jerusalem, not knowing the things that shall befall me there:
Paul's burden for the Jews was so deep that even the sense that afflictions awaited him could not cause him to shake the urgency of the trip.
Paul seems to have known that this trip would be his last - at least as a free man. He told them he knew they would see his face no more. But his burden bound him, compelled him into the danger for the sake of these souls.
And they were not the souls of men who were completely without testimony. There is a church there. To say that our only burden should be for those who have never heard is then, not a Scriptural statement. Paul's burden was for the lost and for other saints. He raised money for those who had already heard the gospel, but were in difficult straits.
What burden for souls binds us? What concern for others compels us to hazard ourselves and give deeply of our own financial resources that others might be born again and encouraged in their walk?