Hey Estelle, thank you for your response!
I think it’s a really good idea to counter their request with telling them about your process instead and also shows they’re dealing with a professional — the process is often more important than the result in itself. Sure, you can make a killer-looking design but does it solve the initial problems? Is it easy to use or is it giving people a good experience? And are there perhaps any new challenges with that design we should iterate? Anyone who’s looking to hire a UX designer should understand this, which is also why the take-home assignment is such a strange thing to request. User Experience Design doesn’t exist without users (people), period. And the companies who can really appreciate those 2 hours you’re willing to give and who will spend it wisely by actually talking with you about your design and reviewing your work is someone worth looking into.

I really hope you find the right match!