The HET is around three months into its investigation into the death of John Molloy in 1996.
The 19-year-old was stabbed to death at Lansdowne Road in north Belfast, a short distance from his Taunton Avenue home, shortly before 12.30am on Saturday August 10.
He had left friends at the nearby Chester Park Hotel to walk home alone.
At first police told his family they were confident they would catch the killers "before the weekend".
However, despite a number of arrests the investigation soon appeared to grind to a halt.
For the first few years after that, around the time of the anniversary of Mr Molloy's death, his father Pat would go to the police station to ask how the investigation was progressing.
But as the years went on it got to the stage where no-one even knew who he was or what he was talking about.
The family were contacted by the HET in August on the tenth anniversary of John's death.
They welcomed the approach but remain too cautious to be optimistic after so many years of disappointment.
"They came out and had a chat but so far they haven't got back to us," John's mother Hilda said.
"They took information and scrapbooks and newspaper cuttings that we had but they did say that they anticipated it would take quite a long time.
"They said it can take up to three months.
"There seemed to be some reason why they were looking at our case at this time."
For the Molloy family this new investigation should be about getting "some sort of closure".
"Even after all this time we just want some sort of justice, although they didn't make any promises," Mrs Molloy said.
"I suppose if they keep you informed and let you know they're doing something it's better than the police who were basically 'There's nothing we can do. End of story'.
"They [the HET team] did say to us when we told them that we hadn't heard anything from police and if we wanted to know anything that we had to go to the police station, that that was totally wrong and they were supposed to let you know once a year if there have been any developments with the case.
"We waited 10 years, so a matter of months you can nearly afford to wait.
"You don't want to keep ringing them in case maybe you're rushing them and stopping them doing a good enough job as they would have if they had been taking the time to do it properly."
Mrs Molloy, who is employed in trauma counselling, said members of the team had also been to her work to learn how to deal with families – although she did not meet them during these visits.
"They were very sensitive and very, very nice.
"The fact that they would go to that trouble is in their favour and I do find them much more sensitive than the police."
