The quartet were all aged 15 or 16 at the time of the offence.
After reporting on the sentencing, trainee reporter James Rose and news editor Julia Collins received emails from angry readers accusing them of “cowardice” for not naming the youths.
The newspaper also had to take stories about the attack down from its Facebook page because people were posting the names and pictures of the defendants.
Wrote Leo: “Readers have struggled to understand how four youths, three aged 16 and one aged 15, could be so vicious, so cruel and so savage.
“They have struggled to understand the leniency with which they were treated by the courts. And they have struggled to understand why we have not named and shamed them.
“Put simply, the law does not allow us to and if we did we would be prosecuted.
“That will not change no matter how many readers email our reporter to accuse him of cowardice and take to social media to do the same.”
The Extra reported how chihuahua cross Chunky was stolen, set on fire and dumped at a rubbish tip with a broken neck and leg in one of the most disturbing cases of abuse an RSPCA inspector has ever seen.
Chunky, pictured above left after making a full recovery from the attack, has since been returned to his owner.
Three of the teenagers pleaded guilty in October to cruelly ill-treating the animal in a way which they knew would cause him to suffer unnecessarily, and were all disqualified from keeping all animals for five years, given a referral order for 12 months and ordered to pay costs.
One of the youths was made to pay £1,000 and the other two £500.
A fourth youth pleaded guilty to the same offences under the Animal Welfare Act, at a trial at Folkestone Youth Court last week.
He was also disqualified from keeping animals for five years and given a referral order for twelve months, plus his father was made to pay costs of £5,800.
In his editorial, Leo added: “The fact is those readers that are sharing the names and pictures of the teenagers involved on the internet are at risk of prosecution themselves.
“And by posting messages about what they would like to do them, you could find yourself facing a fine or worse. One man has already been given a fixed penalty notice for threatening behaviour.
“In that instance it might be you appearing in the newspaper or on our website.
“Sometimes it feels there is one rule for established media and another for the wild west that is the internet. There isn’t. Be warned.”
Leo told HTFP: “We are big enough and ugly enough to take whatever criticism comes our way but James was getting quite a bit of stick very unfairly.
“There is no reason why our readers would understand the law relating to youth courts so I thought it might be helpful to explain – and save James the job replying to lots of emails.”