Ms Anderson’s family had criticised Sinn Fein over the “public humiliation” in telling her to step as aside as an MLA.
A party review also called on party colleague Karen Mullan to quit. Other members of Derry Sinn Fein leadership, including Ms Anderson’s brother and Ms Mullan’s partner, were also asked to step aside.
The two politicians have said they will not stand for the party at the Assembly elections in 2022.
The decision by the Sinn Fein leadership to dump its two sitting MLAs has rocked the party in Derry, with some saying it could damage it further at the next elections.
Others say they won’t vote for Sinn Fein again.
There had been a wall of silence around the decision to remove Anderson and Mullan by the Sinn Fein leadership
But on Wednesday the party finally broke cover with Ms O’Neill saying Sinn Féin had to take action following “damage” in previous elections.
This was in relation to losing five council seats and SDLP leader Colum Eastwood wrestling the Foyle Westminster seat from Elisha McCallion with a 17,000 majority.
In a Facebook post, Ms Anderson’s sister, Sharon Burke, said the family believed she had been “sacrificed” by the party.
She said the party review in Derry “resulted in a massive miscarriage of justice” and the way it was done was “brutal”.
The party “came into Derry to fix problems and left creating more,” she said.
One of Sinn Féin’s most high-profile figures, Ms Anderson has represented the party as an MLA, junior minister and MEP since 2007.
In 2019, she polled 152,436 votes in the European elections in the North of Ireland.
“We needed to do something to fix that (damage),” said party vice-president Ms O’Neill.“We we need to restore confidence in the Sinn Féin team in the Foyle constituency.
“We believe the change we’re going to bring forward will hopefully command the confidence of the people of Foyle.”
The deputy fist minister added: “Both Martina and Karen will be part of that change, but there’s work to do in terms of building confidence.”
She described Ms Anderson as a “first-class republican activist”.
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