The High Court allowed the GCSB to pursue damages, but the men appealed that decision in the Court of Appeal today.
Speaking outside court, Mr Murnane said the men would not pay damages if the appeal was unsuccessful.
"We have no intention of paying a cent, even if I had it, because I don't believe it's a just case."
He said none of the men had the money to pay damages.
Mr Murnane had not held a bank account for 50 years, while his co-appellants were "subsistence farmers".
He said the trio had damaged the dome to stop the spy base from its "dreadful practices" - which he said led to torture and helped to the Iraq war.
"Now the GCSB is suing us to get their gun back. It's like a murderer saying, 'You broke my automatic weapon, I want my gun back - I'll sue you.' They have no moral grounds for suing us. They're doing the dirty work."
Mr Murnane said the GCSB should be accountable to the public, and the "unveiling" of the satellite antenna had been symbolic of that.
The appeal comes as the Government this week seeks to amend the legislation governing the GCSB.
The appellants joined protesters who gathered outside the Court of Appeal in Wellington this morning, ahead of a protest across the road at Parliament.
They were supported in court by more than two dozen people who gathered in the public gallery.
Lawyer Michael Knowles said the men wanted a civil trial to determine whether they owed damages to the spy agency.
In his submissions, Mr Knowles said Associate Judge David Gendall had wrongly decided on complicated areas of law which needed to be heard at a full trial.
He said the judge had also been influenced by seemingly personal fears of "social chaos" if the men's right of claim defence was allowed.
Mr Knowles said the GCSB should have to properly prove its case against the men.
"The appellants crave the right of a full and fair trial of this matter," he said in submissions.
The hearing before Justices Tony Randerson, Lynton Stevens and Douglas White is set down for two days.
