Unable to Delete the Customer Conversation

I was trying to delete the customer conversation, but I can’t delete that.

let me explain the scenario:
consider the customer created the ticket with the subject and description, And then the agent replied to the customer, And the customer replied to the ticket.

Here I was to delete the agent reply, It was deleted successfully, But when I tried to delete the customer reply. It is getting the below error.

    "code": "access_denied",
    "message": "You are not authorized to perform this action."

CURL request:

curl --location --request DELETE 'https://domain.freshdesk.com/api/v2/conversations/26106297173' \
--header 'Content-Type: application/json' \
--header 'Authorization: Basic API_KEY' \
--header 'Cookie: _x_m=x_c; _x_w=23_2' \
--data ''

Can I know what the reason was? I followed the documentation below.

Documentation to Delete the Conversation: