I would respond in writing noting that this is a temp structure therefore not covered by the ARC permit. And that it conforms to aesthetics being natural wood etc.
If they persist, then it’s time to let the board know you will be reviewing every single property for compliance and matching ARC approval. You will find not everyone obtained ARC review so you plan is ‘selective enforcement’.
And I might add, this will run the meter for the management company with your requests for action.
Of course, you ‘might’ be concerned with security and need to install a bright dusk/dawn light on that side of the house. 🙂 Time to have fun.