Your Owners Corporation is in this instance using its By-Laws to assist in maintaining the visual appearance and thereby the overall value of its Building, and if you’re an Owner you have a vested interest in assisting in the achievement of that objective.
Were you to install the folding screen, then you’d be in breach of another By-Law stating that “the owner or occupier of a lot must not, without the written consent of the owners corporation, maintain within the lot anything visible from outside the lot that, viewed from outside the lot, is not in keeping with the rest of the building“.
My advice….. place personal / small items on the clothes-horse inside your Unit in a position where those receive sunlight but from where they’re not visible from the outside (such as behind the balcony door), and convince your “missus” to use the clotheslines for the remainder.
Believe me, that will be much cheaper than the $550 fine that you’ll receive for a continued breach of the By-Laws!