If you really think that the strategy work candidates do in a week’s time for the assignment would be game breaking for the company, you are most likely overestimating it’s impact.
A strategy is nothing without the execution. They might be receiving many such assignments from candidates which don’t mean a thing to them.
It’s just a great way for them to see how you think and synthesise information and present it. And if it’s good enough they will try to see your execution abilities in your prior work experience.
IMHO if you really like the job/product/role , give your best shot and don’t worry about your strategy being stolen or misused. It doesn’t work like that.
P.S : I am in a leadership role in product, have both submitted and received various assignments