Lynda Spence, 27, has not been seen since April 2011, but she was not reported missing until the following month.
Patricia and James Spence told the High Court in Glasgow that Colin Coats came to their home in the days after she disappeared and told them their daughter owed him £10,000.
Mr Spence said Coats threatened to contact the Ulster Defence Association (UDA), the loyalist paramilitary group, if the couple called the police.
Mrs Spence, 56, said Coats was "like a mad man" when she got upset and mentioned the police.
Mr Spence, 68, said: "My wife asked if (Coats) knew where Lynda was and he said he didn't. My wife got all upset and then he started losing the rag.
"She was saying that if Lynda owed him money then she was going to the police.
"He said 'Don't forget, I've got UDA people and London people'. It was a threat."
Ms Spence's parents gave evidence in the trial of Coats, 42, David Parker, 38, Paul Smith, 47, and Philip Wade, 42, who deny abducting, torturing and murdering Ms Spence at a flat at Meadowfoot Road, West Kilbride, between April 14 and 28, 2011.
Mr Spence said he met Coats and another man, Tony Kelly, at Rio Cafe in Glasgow, after his wife received a text, apparently from Ms Spence, claiming to be in London. It said she had spent Coats's money and someone called John Glen had taken £200,000 from her.
He said: "I explained to Coats what had happened and he went pure white.
"He said 'I've got to go outside and calm down'."
Mrs Spence also told jurors Coats made her and her husband hand over their caravan in Burntisland, Fife, as he believed he could sell it for the £10,000 Ms Spence allegedly owed him.
They were later given back the caravan over unpaid fees associated with it, the jury heard.
Mr and Mrs Spence said they reported their daughter missing on May 13, 2011, after a detective told them he was looking for Ms Spence over fraud inquiries. They told the court they did not tell police everything they knew initially but gave another statement on June 2, 2011 when Ms Spence's phone was found in a bin in Kilbirnie, Ayrshire.
Coats, Parker, Wade and Smith are accused of taking Ms Spence from a street in Glasgow on April 14, 2011. They are said to have held her hostage at the flat in West Kilbride, Ayrshire, where they allegedly bound, gagged and assaulted her in an apparent attempt to extract financial information from her.
When cross-examined by Derek Ogg, QC, defending Coats, Mr Spence agreed it was not the accused who mentioned "London people" and said it was Mr Glen. He also said he understood the £10,000 owed came from Coats's parents' funeral fund. Jurors heard later Ms Spence's parents gave her money from the sale of her late grandmother's bungalow to start a business.
She was paying them back by covering their rent, her father said. But when the business folded the payments stopped, putting her parents in arrears.
Mr Ogg asked the witness if he knew his daughter was a police informer, to which he said no.
Mr Ogg asked him if her life would have been safe if people knew she was an informer. Mr Spence said: "Not if she was a registered police informer, no."
Mr Ogg also put it to Mr Spence, who the court heard has spent time in prison, that during the alleged conversation with Coats about getting the police involved, he had said "we don't do police".
Mr Spence denied this. The trial continues this afternoon.