In an interview with Probation, Parsons disputed parts of the summary of facts and was described by the report writer as "entitled and emotionally detached from the offending".
While counsel Alan de Jager said his client was genuinely sorry for what he had done, the judge dismissed that as "window dressing".
Parsons refused to divulge why he had swindled his victims and would not go into detail about his personal circumstances at the time.
"The only conclusion I can draw is that this was offending for greed rather than need," Judge Robinson said.
Parsons was introduced to the Syrian family in 2016 through a Red Cross support worker.
"Over the ensuing few years, he ingratiated himself with [them], building up a friendship where they trusted and relied on him, especially as the victim struggled with English," court documents said.
In February 2019, the family obtained a credit card and within months Parsons swooped in, claiming he could help manage the finances.
The defendant first made cash withdrawals before using the account to buy a $100 barbecue and then came up with a plan.
He "gifted" the item to the refugee family and they agreed to pay him back in small cash sums.
Over the next couple of days, Parsons ramped up the thefts, withdrawing $1800 from automatic teller machines.
The defendant's final insult was to buy two cellphones using the card. One he kept for himself and the other he sold back to the unwitting victims.
Judge Robinson said the family received repeated reminders of the ordeal in the form of emailed reminders about their debt.
The fraud came to light after Parsons was jailed for 19 months in December last year for scamming a 90-year-old woman out of nearly $13,000.
Similarly in that case, the victim allowed him to assist with her finances and he set about bleeding her accounts dry.
Judge Robinson this week was concerned to hear Parsons had recently been acting as a caregiver for his ailing partner and had full control of her finances too.
He added four months and three weeks to Parsons' prison term and imposed release conditions that barred him from controlling any bank accounts other than his own.
The victims were out of pocket $2800 but the judge imposed reparation of $1500, noting the defendant already owed more than $18,000 to others he had defrauded.
