The update came last night as police officers handling the investigation were criticised by a father whose son and grandson were arrested on suspicion of her murder.
Greg Elsey, whose ex-wife Rosemary Dinch was also arrested by police, said the ordeal had "ruined their lives" as "mud sticks".
The trio, all of whom were known to Pope, were released after being taken into custody last week.
They remain under investigation by Dorset Police, who are treating her death as "unexplained".
It comes as Gaia's cousin Marienna Pope-Weidemann vowed to get justice following the heartbreaking discovery as tests on Gaia's body are ongoing.
She wrote on Facebook: "We hold you in our hearts forever. Know you are with Nan & Pops now but miss you beyond words. You will have justice. Fly on."
Maya Pope-Sutherland also paid tribute in a Facebook post in which she wrote: "Can't find any words right now. Gaia is my everything and I am heartbroken. I thank everyone who was involved in searching for my beautiful twin. Going to make her so proud."
Greg Elsey, 69, said his family intends to pursue legal action over the arrests of 71-year-old Rosemary, his son Paul, 49, a carpenter, and his actor grandson Nathan, 19, for alleged smears on their character.
"The officers running this investigation seem to be a bunch of wooden tops," he said at his home in West Wellow, near Romsey, Hants, today after admitting his heart went out to Gaia's family.
"We have only ever tried to help - both Gaia and the police.
"But what my family has been through due to Rosemary's act of kindness in inviting Gaia into her home is terrible."
He went on: "We will take action for wrongful arrest. This has ruined their lives. Mud sticks doesn't it.
"Police should have said they were talking to someone who was helping them. Instead they said they arrested people on suspicion of murder. In terms of a smear on someone's character, it really doesn't get much worse, does it."
Specialist search teams found Gaia's body on land near Swanage, Dorset, close to where clothing identified as hers was located near cliffs on Thursday.
Hundreds of volunteers joined her family, including her father Richard Sutherland, in a mass search for her on Saturday afternoon prior to the discovery.
Gaia, an epilepsy sufferer, went missing nearby on November 7. Her sister Clara Pope-Sutherland, 21, said she was the "absolute light of my life" and described her as "intelligent, beautiful and emotionally wise".
A spokeswoman for Dorset Police said it would be wrong to speculate on the cause of Gaia's death until a post mortem examination had been completed, when an update would be issued.
Det Supt Paul Kessell said: "This will guide the investigation in respect of the circumstances of the death, which at this time remains unexplained."
