Counsel for the families said they were horrified at learning of an attempt to include the level of damages as an issue at the civil retrial of two men being sued over the atrocity.
Judges in the Court of Appeal were told the question of liability alone should feature in the case against Colm Murphy and Seamus Daly.
The two men are defending an action brought by relatives of some of the 29 people, including a woman pregnant with twins, killed in the 1998 Real IRA bombing.
The retrial, ordered after their appeals against being held responsible for the bombing were upheld, is due to get underway at the High Court in Belfast in October.
Two other men found responsible in the initial landmark ruling, Michael McKevitt and fellow dissident republican Liam Campbell, failed to have the findings against them overturned.
They are now attempting to take their case to the Supreme Court in London.
No-one has been successfully criminally convicted of the bombing which devastated the County Tyrone market town.
In June 2009 McKevitt, a convicted Real IRA leader serving a 20-year jail sentence; Campbell, a farmer from County Louth currently fighting extradition to Lithuania over an alleged arms smuggling plot; Murphy, a Dundalk-based builder and publican; and Daly, from Culaville, County Monaghan, were all found liable for the bombing in a civil ruling.
Mr Justice Morgan, now Northern Ireland's lord chief justice, ordered them to pay £1.6m in compensation. But in July last year the appeals by Murphy and Daly were upheld.
Lawyers for both sides in the retrial returned to the Court of Appeal on Thursday over claims that Murphy and Daly are seeking to reopen the level, or quantum, of damages in the case.
Brett Lockhart QC, for the plaintiffs, said: "We were horrified by that prospect, because of the appalling vista of potentially having plaintiffs re-examined and also having to give evidence again."
He contended that it would be "absurd" to allow the issue to feature and possibly lead to varying findings against different defendants.
Mr Lockhart stressed how his clients had gone through the events in the witness box once before.
"We are very sensitive about re-traumatising the victims who have already given evidence," he added.
"It's an experience they wish never to happen again."
Dermot Fee QC, for Murphy, responded by insisting the issue of quantum had always featured.
He outlined how the "diagnostic labelling" of post-traumatic stress disorder to all the plaintiffs was to be challenged.
"Our argument was, and remains, that it was inappropriate," Mr Fee said.
The barrister also argued that because a retrial was ordered all issues could be re-opened.
However, Lord Justice Higgins, sitting with Lord Justices Girvan and Coghlin, stated that it was intended to deal with the issue of liability only.
He said: "We are reinforced in that view by the principle that there should not be inconsistent verdicts, and by reason of the fact that there was no appeal against the quantum in the first instance."
He directed that the court's views should be passed to the judge due to hear the retrial.