The high-profile couple received anonymous threatening letters sent to their London home, a court heard.
The couple are trying to have bankruptcy declared in Britain and Bank of Ireland is opposing their bid in the High Court in London.
Bank of Ireland argued that it was entitled to the contents of two properties -- the couple's home in Killiney and a house in London where they now live -- as part of its efforts to recover a €75m judgment granted to it last year.
Mr O'Donnell and his wife, Dr Mary Patricia O'Donnell, claim the houses and their contents are owned by the couple's four adult children via trusts.
But the bank said that those trusts were a "sham".
Dr O'Donnell said that she has been unable to find a tenant for the listed eight-bedroom townhouse in Westminster. The couple pay £4,000 (¤4,900) a month in rent under a tenancy agreement with Vico Barton -- a Swiss-based trust set up for the couple's children.
Gabriel Moss, for Bank of Ireland, which opposes the petition, asked if this rent was "not absurdly low" for such a property in a key location.
But Dr O'Donnell said: "It isn't absurdly low, and I'll tell you why. We could not rent it out for £4,000 a month.
"It is very hard to rent properties at high prices."
Rent has been paid over the last two months, she insisted, though previous rent had been "offset" against the cost of running the property, which has a a swimming pool and three kitchens.
The four-storey property was put up for sale for £13m (€16m) two years ago.
The O'Donnells have said that their centre of main interest is in London and they should be allowed to declare bankruptcy there. Bank of Ireland wants them to face bankruptcy here.
Dr O'Donnell said the bank's actions were "unwarranted and unbusinesslike".
When Mr Moss, suggested that she was "pretty good at propaganda yourself", Dr O'Donnell said: "It is not propaganda, it is the truth".
The O'Donnells contend that the trust set up to own their home in Gorse Hill in Killiney had been suggested by Bank of Ireland, after the couple "nearly drowned" on Lough Corrib in 1995.