Amy Cluskey had part of her nose and upper lip ripped off during the attack.
The judge questioned why police had not told Lee Cluskey, 19, that Mooch was illegal after it killed a cat months before the August 2014 incident.
Cluskey, of Mount Pleasant, Waterloo, who pleaded guilty to possessing a fighting dog got a suspended jail term.
He also admitted a charge of having a dog dangerously out of control and was told his custodial sentence would be suspended for nine months.
The court heard he had contacted Merseyside Police following the incident with the cat.
In response the judge, Recorder Simon Medland QC, said: "Last year, I am very surprised the police did not realise this was in fact a pit bull terrier, which is a prohibited fighting dog.
"It has, to my lay eye, all the appearance of one. It seems a most odd conclusion they came to. The dog has not changed in the last 12 months."
He said an expert "very clearly" identified it as a pit bull breed.
"Quite why the police missed that in 2014 I don't know, but they did," the judge added, describing the information they gave to Cluskey as "duff".
He said Cluskey's remorse was genuine and "one could almost say palpable".
The court heard he told police he turned his back to get the dog's food when he heard his sister screaming.
"The dog had jumped up at her face and latched on," he said.
He prised its mouth open, struck it on the head with his elbow and pulled its tail before forcing it away and locking it in a bathroom.
His sister lost some of her gum and front teeth and underwent emergency surgery, spending a week in hospital and having a series of operations.
A Merseyside Police spokeswoman said: "We note the findings of the court case.
"An internal review of the police response to an animal attack in Bootle in August 2014 is to be conducted to establish the full facts of the matter.
"As such it would be inappropriate to comment any further at this time."
A six-year-old girl was savaged by her brother's pit bull dog after police failed to tell him it was a banned breed, Liverpool Crown Court heard.