Is it permissible to accept financial compensation from an airline for a flight delay that led to the disruption of an important appointment, knowing that the ticket price was not paid by the individual himself?

If the request for a ticket refund is for compensation for damage, then it is permissible, supported by evidence from the Qur’an and Sunnah, such as: (So whoever has transgressed against you, transgress against him in like manner as he transgressed against you), and (And if you punish [an enemy], punish with an equivalent of that with which you were afflicted), and (And the retribution for an evil act is an evil act by the like of it). So, if the delay was due to negligence and carelessness, and you incurred damage, then it is permissible for you to take compensation equivalent to the actual damage, not for profit. And pardon and forgiveness are better, as Allah Almighty said: (But whoever is patient and forgives, indeed that is of the matters [requiring] determination). If the damage was inflicted upon the company, then compensation is its right, and if it was upon both of you, then it is your right.