Ross Monaghan, 35, was shot in the back in a targeted attack outside St George’s Primary in the Penilee area of Glasgow at about 9.05am on January 16.
He was approached by a man pushing an empty buggy who pulled out a gun and fired at him before fleeing along Hollybush Road.
About 30 detectives and uniformed officers returned to the area between 8am and 9am on Monday to try and jog the memories of parents, and trace any more witnesses to the attack.
The victim, Mr Monaghan, was cleared of killing gangland figure Kevin ‘’Gerbil’’ Carroll in 2012 after a judge ruled there was no case to answer due to insufficient evidence.
He left hospital after brief treatment last Monday.
Detective Chief Inspector John Kennedy said it was a “difficult” investigation with some people fearful of coming forward with information.
He said: “Anyone that comes forward with information we will treat in confidentiality.
“This is a difficult type of investigation to get people to come forward and that’s why I would suggest if they are fearful of approaching the police here then they can contact us outwith this environment or through Crimestoppers.
“Parents are still concerned regarding what happened here last Monday morning but by the police presence and the intensity of our investigation, we’re hoping that we’re reassuring them.”
Detectives are trying to establish if the suspect made off from the scene in a car.
“Our enquiries so far have shown that the suspect is believed to have been in the area, outside the school, on Friday January 13 with the buggy, so I’m appealing to parents, local residents, or anyone who was in the area that day and who may have seen something to contact us,” Mr Kennedy added.
“It’s possible the suspect made off in a vehicle and I’m asking people in the surrounding areas to think back and consider if they noticed anything unusual or suspicious.”
A bullet recovered from inside the school grounds is being studied for more information on the weapon used.
Mr Kennedy said: “There was a bullet recovered in a tree, about 6ft off the ground, just inside the school gate.
“We’re still waiting on the ballistics report which will confirm the exact weapon used.”
Reports at the weekend suggested a man arrested over other gang-related incidents would be questioned for any knowledge of the shooting.
Mr Kennedy said: “We look at everyone who is arrested, whether there’s connections, and we take it one step at a time, and we’re very thorough in our investigation.
“There’s been no arrest specifically in relation to this.”