Presuming they were careful to preserve the area of the hat surface, likely very authentic. If it doesn't have any creases, there's precious little you can do t

Presuming they were careful to preserve the area of the hat surface, likely very authentic. If it doesn't have any creases, there's precious little you can do to reshape a given convex piece of felt. More oblate/more circular is really about it. Now, felt can be reshaped easily with steam-level heat - but that would require a conscious effort.