Majella O’Hare, from Whitecross, had been walking to church on August 14 1976 when she was struck in the back.
At the time soldiers claimed the shooting had been in response to an IRA sniper attack. A soldier was later charged with manslaughter but was acquitted in court.
In 2011, the UK government issued an apology to the O’Hare family in a letter which acknowledged the soldier’s courtroom explanation was “unlikely”.
Now the family say they want the record set straight on what happened to Majella, and have written to the PSNI requesting an independent investigation.
Majella’s brother Michael has vowed to fight for justice for his sister. “If it weren’t for the actions of the soldier, she would still be with us,” he said.
“We live with the pain that we will never know the potential of her life. The apology acknowledged the wrongdoing, but neither this nor the historical enquiries report which prompted it provided us with the full truth of what happened. It didn’t give us the justice and accountability we are entitled to.
“I hope this will now come and give my family and I the peace we seek”.
The family is being supported by Amnesty International.
Grainne Teggart, the group’s Northern Ireland campaign manager, said the story of Majella should be a “matter of national shame for the UK”.
“It is utterly appalling that the family have been left without justice for nearly 44 years,” she said.
“The loss had a devastating impact on her family.”