I know very little about Ty other than what I read on his FB from time to time. He is from South Korea, very wealthy, close family, apparently he retired from some successful business, and decided what he wanted to do with his free time is work with reptiles, many of which are locale specific iguanas that are considered vulnerable or threatened.
I do not know what type of culture his beliefs are based on, American or Korean? I do know that as an American it would be nessesary to fullfil his obligation to the OP to the letter, and err on the side making her happy. She really wanted one of his Tegu, not $3k, and when Ty could not provide the animal, he should have given her what she wanted instead. I do not know how this would be handled in a Korean culture, but as we have seen many many times just recently, some succesful people have a very hard time addmiting they were wrong, and/or appologized. Maybe it is pride that is keeping him from doing what we all see as being the right thing, I am not sure?
I think he has gotten bad advice from someone close to him. If I were to make a suggestion to him, I would say. "pay her the $3000, it is the right thing to do" otherwise you will have people like
King Joffrey trying to drag your name through the mud until he tires of it,
and trolls someone else