The force said Ms Reed, a geophysicist, had no involvement in any criminal activity.
It said the man, described as wearing glasses and holding a pizza box, asked Ms Reed, who lived in Willow Way, to confirm the address before she was shot at close range five times.
Crimestoppers is offering a £20,000 reward for information that leads to the conviction of those linked to the murder.
Mick Duthie, director of operations at the charity, said: “We would like to see justice for Karen, her family and friends.”
Ms Reed’s brother has previously appealed for help to find the “coward” who killed his “gentle, compassionate and warm-hearted” sister.
In a statement on Crimewatch Live in 2021, he said: “Karen answered her front door to someone who, without asking her name, shot her dead.
“A moment earlier, she had been curling up with her cats, having a glass of wine, catching up with a friend.”
He described her leading a “blameless, quite ordinary life” and said she deserved justice.
