"She's a great person. I don't understand how something like this can happen," Amanda Palumbo said.
An unidentified body was found burning on the side of a rural road in northeastern Connecticut last Friday.
Investigators broke the news to her parents on Wednesday that the victim was Becky and that she had been murdered.
"We just lost our daughter to some psychotic maniac," said Larry Ross.
"She's the nicest person. No one knows who could hate Becky enough to do something like that," her brother, Damian, said.
Becky's friend Nicole Longo was one of the last people to see her alive, when they went out last Thursday night.
"I left because I had to go to work. She said, 'I'll be ok. I'll see you later,'" she said.
Becky was last seen at the bar at Butcher Boys in Holbrook. She was with a young man friends say she'd been dating casually for the last two months. Police believe he dropped her off at home at 3:15. By 6:00 a.m., she was gone.
Becky's friends remember her as a warm person, dedicated to helping the elderly in her job as a nursing assistant. They can't fathom who would want to kill her.
"This is so crazy. How does this happen, so I look at everyone," said Desiree Gunn.
Police on Long Island and in Connecticut are following all leads, but they have not made any arrests.