The High Court in Edinburgh has heard how John Docherty, 49, chatted to cook Elizabeth McCafferty just weeks before his arrest.
The conversation was recalled yesterday by Mrs McCafferty, 53, who was one of the last people to speak to Ms Doyle before her death in June 1986.
At that time Mrs McCafferty helped run a mobile snack bar in Greenock town centre.
She had seen Ms Doyle, who had been to a Sunday night disco in the Celtic Club in Laird Street, walking towards the town centre just after midnight.
Mrs McCafferty went on to work as a cook at an children's centre in Greenock.
Docherty, a driver for Inverclyde Council, would ferry youngsters to and from the centre as part of his work. She regarded him as a friend and they chatted on a daily basis.
Mrs McCafferty said she had received a phone call last year asking if she could think of anything to add to her earlier statements.
Mrs McCafferty said she told Docherty about the call, possibly six weeks before his arrest.
"I think, if I remember right, John had said: 'Do you think they will ever get anybody for it?' and I said: 'After all this time, I don't think so.'"
Docherty now of Hunters' Quay, Holiday Village, Dunoon, denies murder.
The trial will continue on Monday.