Witnesses Catherine "Dolly" Eaton and her daughter Charlotte Peoples told the inquiry the calls were made to their homes.
Mrs Eaton said she received around 20 calls, some at around 5am, over a period of about three months, and they only stopped when she changed her telephone number.
She also reported at the inquiry hearing in Donegal town that the gardaí had said they would look into the incidents soon after they happened, adding: "Five or six years later, I am still waiting," she said.
Mrs Eaton said that she would like the tribunal itself to look into the silent phone calls, and counsel Patrick Barr said that would be done.
The calls to her home came after the arrests by gardaí of her daughter Charlotte and son-in-law Michael Peoples when a murder investigation was launched some time after the death of Mr Barron on October 16, 1996.
Charlotte Peoples said that she had unsuccessfully asked the callers one of whom had asked for money to identify themselves and had then gone to the gardaí about the affair. She was told by an officer to "play along with it".
Mrs Eaton recalled that she had been babysitting for her daughter on the night Mr Barron a relative of hers had died, and she had been upset on hearing the news.
The tribunal is examining in detail how the Barron death was investigated, including claims that garda officers were late arriving at the scene of theincident, and failed properly to preserve the scene after the discovery of the body, as well as their reasons for regarding two men as murder suspects and other apparent flaws in the operation, among them questions about the use of informers.
The present module of the proceedings is being staged in Donegal for the convenience of locally-based witnesses.