Using donated fabric, volunteers have so far created a vibrant 72-foot square patchwork of personal messages and depictions of the people who died.
Their sewing techniques have been inspired by the National AIDs Memorial quilt and rugs made by African-American slaves.
They aim to expand it to 220 ft – the height of Grenfell Tower.
Ms Greenidge told the PA news agency that many people affected by the tragedy have found “comfort and reassurance” in the sewing sessions.
The aim was to be a hub where people could come and release and express these emotions through creating and colour
She said: “All the alternative groups – healing groups to help support them in their recovery – have closed down before the end of the inquiry.
“That’s why a lot of us have little seeds of anger.
“The aim was to be a hub where people could come and release and express these emotions through creating and colour.
“I know what I get from colour being an artist.
“There’s something mystical and magical about seeing it all blend together.
“I just wanted them to absorb that energy, to remind them that there are people in the community that love you and support you all – and we’re not going to go away.”
Ms Greenidge lost several close friends in the fire, including 12-year-old Jessica Urbano Ramirez, who went to school with Neveah – her friend’s granddaughter who she looked after like her own.
Jessica’s name was the first she embroidered on the quilt.
Speaking about Neveah’s reaction to the death of her schoolfriend, Ms Greenidge told the PA news agency: “I had never heard a child wail like she did.
“It was deep. We used to tell her ‘let it go, let it go’.
“She used to sit on top my wardrobe and just… yeah.”
Ms Greenidge pointed to another name on the quilt – Moses – as 63-year-old grandfather Raymond Bernard was known in the community.
She said: “Moses was incredible. Everybody knew him.
“What we found out at his end, was that there were a lot of residents that ended up in Moses’ flat. One of them was Jessica.
“And he laid the children in his bed, and that’s how they were found.
“The children went to his flat during the fire because they all knew and loved Moses.
“They went for comfort, because Moses might know what to do – and he did.
“He knew to comfort them while they passed over.”
Ms Greenidge said her daughter, Charlie Manning, 38, had been visiting friends in the tower on the night of the blaze, and ran to alert her after escaping.
They watched the blaze in horror afterwards in scenes that Ms Greenidge described as “like a movie”.
Speaking about her daughter, she told PA: “She doesn’t talk about it that often.
“For quite a few days after she just had a fixed stare.
“It feels a bit overwhelming already, because there’s a lot going on in the community.
“It’s a difficult time, but nothing compared to what the bereaved are going through, so we’re there to support them.”
Ms Greenidge said pieces of the quilt will be displayed around London to mark the fifth anniversary of the fire on June 14, 2022.
She is hoping the striking duvet will catch the attention of the BBC’s Sewing Bee which could help them reach their 220-foot target.