A Florida judge will decide Wednesday whether Petito's parents have enough evidence to pursue legal action and send the case to a jury.
"The Laundries should be responsible for their conduct and what they did after they knew that Gabby was dead and where her body was located," said Patrick Reilly, the Petito family attorney.
Investigators with the FBI say last summer, Laundrie strangled Petito to death in Wyoming and returned home to Florida without her.
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Her disappearance sparked a nationwide search, but Laundrie and his family refused to speak with law enforcement or Petito's parents before Laundrie himself disappeared.
Authorities later found his body in a nearby swamp next to a handwritten confession note, and an autopsy report later determined that Laundrie died from a self-inflicted gunshot wound.
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The Petito family is now accusing parents Christopher and Roberta Laundrie of "intentional infliction of emotional distress." The suit alleges the couple knew their daughter was murdered but said nothing, instead calling a lawyer and cutting off communication with Gabby's mother, Nichole Schmidt.
"They refused to return calls, and then they blocked her on her cell phone and blocked her on Facebook," Reilly said.
Neither Christopher and Roberta Laundrie commented publicly after Gabby's disappearance.
Still, they're seeking to dismiss the case, with their lawyer calling the Petito family lawsuit "baseless."
"The law does not require an individual to speak to a third party under any circumstances," the Laundries' lawyer Steven Bertolino said.
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He would not confirm whether the Laundries knew what happened to Gabby before her body was found but said he advised Christopher and Roberta not to speak with anyone, including Petito's family
"You have the right to remain silent," Bertolino said. "You have the right to allow your lawyer to speak for you. And you should not be liable to any third party, whether it's the family of the victim or whether it's a victim."
ABC News Chief Legal Analyst Dan Abrams said Petito's family faces an uphill legal battle.
"The lawyer for the Laundries makes a fair point ... As a legal matter, you don't legally provide information to help in an investigation. To sue over that is very unusual, very hard to win," Abrams said. "The lawsuit is pretty broad and pretty vague, which is why today's hearing becomes so essential if enough here as a legal matter to send this to a jury."
In December, Schmidt spoke to ABC News about turning her daughter's death into a mission to fight domestic violence and find missing people.
"I don't want to see this happen to another person. Just awareness alone is giving people the strength," she said.