[spoiler] They didn't really dwell on Barnabas' disappearance much at all after 1897 ended, just moved to the next storyline. Some characters knew he went to the past and didn't really question it. Though they still remembered Quentin's haunting even though history was changed and his ghost shouldn't have been remembered at all. It would have been nice if they showed Ezra Braithwraite or Janet Findlay still alive in cameo appearances at least.
During the Summer of 1970, Quentin's ghost is apparently forgotten as the timeline seems to have caught up to the present. [/spoiler]