"He (Penteado) received £24,077.60 in housing and council tax benefit he was not entitled to," Miss O'Neill said.
"He failed to notify the borough council of the money coming in."
The court heard the council, which brought the prosecution, would be seeking to recover all the cash and Penteado had paid back £210 already.
No mitigation was put put forward by his solicitor, Terrence Scanlan, at the hearing.
The Portuguese-born presenter, who was wearing a white shirt, black tie, black trousers and a black jumper and carrying a black biker jacket, left court without comment.
Two weeks ago, Dorset police applied for an arrest warrant after he failed to respond to letters of enquiry sent to him by Bournemouth Borough Council.
He was sent a court summons to appear before Bournemouth Magistrates' Court to answer several charges of fraud.
But he failed to show up and a warrant was issued for his arrest. Dorset police confirmed they were making enquiries to trace Penteado so they could arrest him.
On June 14, Penteado handed himself into the police and insisted it had been a 'misunderstanding.'
He said at the time: "It's all a misunderstanding that's causing a lot of grief for my family.
"There is no arrest warrant. I've been to the police station and I've not been arrested."
Penteado started working with Mr Allwright in 2001 and had been an integral part of Rogue Traders and Watchdog since then.
In the last series of Rogue Traders, he and Allwright confronted eight business owners they felt were ripping-off the public across the UK.
When he is not working on Rogue Traders he works as a private investigator in the UK and abroad.
The case was adjourned until July 17 at Bournemouth Magistrates' Court.