In a statement they wrote, "We have sent you a private message and ask that you respond to us privately. We know that you have read our previous communications, John Cantlie made references to them in October."
They were referring to an Islamic State of Iraq and Syria (ISIS) video, part of a propaganda series featuring the British journalist, who is still being held. In the video, Cantlie directly quotes emails between ISIS and the families of hostages.
It's among the communications the Muellers had with ISIS over the last 18 months, working to free their daughter.
The 26-year-old was taken in Aleppo, Syria, on Aug. 4, 2013, leaving a hospital run by Doctors Without Borders.
She had arrived the day before from Turkey with her boyfriend, who the medical aid group said was a technician contracted to perform repairs at the facility. They weren't expecting him to bring a friend.
The two spent the night, and the next day, the charity said it organized transportation to the Aleppo bus station, from where they were to depart for Turkey. They never arrived at the bus stop.
Her boyfriend, who hasn't been identified, was released some months later.
It wasn't until May of 2014 that Kayla's parents received their first contact confirming her captivity and that she was still alive.
Then, in early July, U.S. special operations forces launched an unsuccessful rescue attempt to save Western hostages near Raqqa.
They didn't find anyone, but according to a U.S. official familiar with the operation, evidence collected at the site included strands of hair believed to be from Mueller.
In August, the world watched as ISIS began releasing videos showing the gruesome killings of its Western hostages.
A few months before she was kidnapped, Mueller gave an interview to her local paper in Arizona. She explained why she was helping Syrian refugees.
"When Syrians hear I'm an American, they ask, 'Where is the world?' All I can do is cry with them, because I don't know," she said.
She goes on to say, "For as long as I live, I will not let this suffering be normal."
Mueller had been in Turkey since December 2012 working for two different aid groups helping Syrian refugees.
It's unclear if she was working for any of them when she was captured, but at this point, that August 2013 trip is the only known time she went into Syria.