The Commercial Court has been told that "huge" six-figure sums passed in and out of accounts held in the joint names of Seán Quinn's daughter Ciara and some of her children in 2011 and 2012.
Lawyers for a receiver appointed over the assets of members of the Quinn family said an explanation was sought for the transactions, but one was only recently provided.
The transactions were described in court as "high value" and "highly unusual".
The Quinns argue the sums have nothing whatsoever to do with assets of their international property group or any assets which are the subject of legal proceedings between them and the Irish Bank Resolution Corporation, formerly Anglo Irish Bank.
The Quinns were seeking variations on the freezing orders on their accounts subject to various conditions.
The freezing orders were granted in July 2011.
Agreement on the variations subject to conditions was reached.
Barrister Ross Aylward, representing the Quinns, said a suggestion by the bank that around €6m passed in and out of the accounts was based on "double counting" lodgments and withdrawals and the sums involved were nowhere near that amount.
He said the delay in providing an explanation was a result of an innocent oversight.
He said the Quinns had to deal with much complex litigation and the receiver had not indicated there was any urgency in relation to providing an explanation.
The payments referred to included a €735,000 credit payment dated May 2011, from the account of a wind farm company to an account held by Ciara Quinn and a daughter of Ms Quinn.
Another payment, dated January 2012, was a €320,000 debit transfer to an account in Dubai with the beneficiary named as Market Study Solar Energy.
There were substantial six-figure debit payments to lawyers.
A credit payment of €320,000 was made in April 2012 to Ciara Quinn's own account from an account of a company in Dubai.
The IBRC's special liquidator, Kieran Wallace, said in sworn documents submitted to the court that an analysis of the accounts showed they were not maintained for the benefit of the children in question and involved extraordinary transactions whereby vast amounts of money were being channelled in and out of the children's accounts.
The accounts were disclosed by the Quinns in the autumn of 2012.
In further documents submitted to the court, Aoife Quinn said the money lodged to the accounts came from Cranaghan Property Management Limited, Quinn Windfarm Limited and Snugborough and IBRC "well knew" these companies had no connection to the legal action.
Full details of the agreement between both sides on the variation applications will be put before Mr Justice Peter Kelly tomorrow.