Thomas Cook faced the allegation after the company's legal team said the mother and father had a duty to supervise their daughter, who was 14, during the 2009 trip.
The family have launched a £250,000 claim against the firm after the girl alleged she was raped by a security guard on a sun bed after being earlier plied with drink by bar staff at the Gran Caribe Club Cojimar resort in Cuba.
Yesterday, at the Court of Session in Edinburgh, the company's retail arm faced criticism after it successfully moved to have the parents named as third parties in the claim.
The firm's counsel, Robert Milligan QC, told a judge at the court: "The defender's case, very simply, is that the pursuer's parents were under a duty to supervise her."
He said that there seemed to be a suggestion in the action that the Cuban hotel where the girl was staying with her parents during the all-inclusive break in 2009 had "assumed parental duties over this child".
Mr Milligan argued it was in the interests of justice to conclude everything in "one fell swoop."
The 19-year-old alleged victim's QC Angela Grahame said her client required considerable help from her parents as a result of the rape. She said: "She was 14 at the time of the rape and is now 19. She has serious psychological problems."
She argued such a move would "force a wedge between a young, vulnerable woman and her parents who are providing a significant level of emotional support".
Ms Grahame said [Thomas Cook] was also embarking on "what one can only say is a cynical attempt to force the pursuer to drop the action" rather than pursuing litigation without the support of her mother and father.
Lord Armstrong said he appreciated the position of the teenager and her vulnerability, but he would allow the service of third party notices. The judge said the interests of justice favoured the firm in the matter and added: "An issue arises which is a legitimate issue and which the defenders are entitled to have ventilated and addressed by the court."
The girl's parents booked a holiday for themselves and her at a branch of Thomas Cook in Lanarkshire in 2008 before flying out to the resort in Cuba in 2009.
Guests were given coloured wrist bands, with yellow for adults and green for minors, to access food, drink and services. Anyone wearing a green band was not allowed alcohol. The girl was given a green band, but another youngster, who was also a minor, was given a yellow one.
The two girls arranged to go to a disco at the resort and were given a 1am curfew by their parents, it is said. It is alleged the disco was cancelled and they went to the foyer where it is said they got alcoholic cocktails from bar staff despite it being a criminal offence to serve minors in Cuba.
It is maintained by the family's lawyers the staff did not take "reasonable care" of her safety. The girls were later followed by men, one of whom allegedly carried out the attack.