Personally, I think it is offensive on several levels.
It is offensive in that it suggests that being a woman is about having periods. True, most girls think their childhood ends and being a grown up begins, when they have their period. But seriously, to define a woman by a period?
It is offensive as somewhat overly singular, not to mention inaccurate. Few people know when any woman is having her period or even if, but anyone knows that is a woman.
It is offensive in it suggests that transgender woman yearn for periods. There are many things I dislike about what I have to live with, not having periods isn't one of those.
It is offensive in it's portrayal of a transgender woman. It is obvious that it is a transgender woman. The actor is clearly attempting to create a very unsympathetic portrayal. But more importantly, the media portrayal of transgender invariably seeks to portray the individual as failing. As if it is daring any of us to object. Well, this transgender woman had broad shoulders, a deep voice, loads of facial and body hair, ugly bits and the stink to match. But I am still a transgender woman.