They initially offered $5,000. The reward now stands at $20,000.
WATCH: Family increases reward
Editor's Note: This story includes details that may be disturbing.
Relatives pleaded with the community to come forward with any information about 81-year-old Thana Muhammad's silver 2012 Honda Accord, with license plate R881876.
Her daughter, Ashanti Chimurenga, and her granddaughter, Camille Durham, said they believe the vehicle was stolen from her home in the 10000-block of South Forest Avenue on June 5 or 6. The vehicle was recovered by police on June 14 in the city's Lawndale neighborhood.
Durham said anyone who saw the person driving that car or anyone who was given that car during that time period should contact police. They said anyone who saw Thana Muhammad in the two weeks leading up to her death and has pertinent information that could help the investigation should come forward
"These are all small things that maybe you saw and you don't realize they're part of a bigger picture. These are the type of tips that we need. We are increasing our reward to $20,000 because we need something from the community. Someone knows something. As the saying says, the truth shall set you free," Durham said. "That's what we need here. We need someone who knows something to step forward so that we can end this senseless violence and give my grandmother, Thana Muhammad, closure. This was a brutal, brutal murder, Chicago. This was brutal. We need your help."
"If you can hide my mother's killer when she was put in two bins, you need to also have some light shed on you, because our community deserves to be safer. We must stand up as individuals. No one is going to protect us if we don't protect ourselves," Chimurenga said.
Muhammad was a retired radiologist. Her relatives said she was a beloved fixture in many communities.
"This is Thana," Chimurenga said, holding up a smiling photo of her mother. "Not two storage bins. Not a story. This is my mother. The last three months of her life - 81 - gorgeous, beautiful, radiant and clearly showing you that she had a zest for life."
Muhammad, also known as Jean or Mattie Chandler, was found murdered in her home. Police said she sustained "severe trauma to her body."
Officers making a well-being check shortly before noon on June 10 discovered her body in storage bins in the basement of her home. Sources told ABC7 Eyewitness News she had been "cut in half."
"She did not deserve this, Chicago," Durham said. "This is a monster. This is a monster."
Chicago Police Superintendent Eddie Johnson said she may have known her killer.
"They put a lot of thought into what they did," Johnson said. "The crime scene was very clean. They took their time and meticulously tried to hide what they had done."
The Cook County Medical Examiner's Office has not determined how or when the woman died. Investigators have not yet determined a motive.
"My mother was a good, kind, heroic woman," Chimurenga said. "I don't know why my mother had to die such a horrendous death."
"Beautiful person. Strong. Independent. She had ties on the West Side and the South Side. I want to stress that," said Trina Mangerum, Muhammad's niece.
Muhammad, a retired radiologist who lived alone, owned several properties on Chicago's South and West sides. She moved back into the house on Forest about two weeks ago, after renting it out.
Muhammad's purse was also stolen.
Family members said they can't imagine who would want to hurt Muhammad.
Police have reviewed several angles of home surveillance video. Area South detectives are handling the investigation.
Anyone with information about the murder should call detectives at 312-747-8271.