Mytrip Didn't Correct the Typo on My Flight Ticket

I have booked tickets for three people through the Mytrip travel agency for the period from August 19 to September 1, with the PNR number UJKD7J and flight number TK 1591. I misspelled a letter in my daughter's name. While trying to contact Mytrip, they insist that Turkish Airlines (THY) should make the correction.

Upon calling THY, they claim the travel agency should handle the correction. Despite suggesting to cancel and rebook, they say it's not possible. The agency states that up to two letters are not an issue, while THY insists it is a problem. Can correcting a letter truly be this difficult in the 21st century? It's as if both parties are at odds, with customer representatives blaming each other. Such a fiasco should not be.

If airlines are so dissatisfied with travel agencies, why grant them the authority to sell tickets? Who will resolve my problem now? Regardless, I will pursue legal avenues to assert my rights and broadcast this issue on all social media platforms. How can a major airline like THY escalate such simple problems and trouble people? I don't understand.