Coca-Cola® can. Samsung® can. McDonald’s® can.
Your company can’t.
So just don’t mention that big event going on down in Brazil. Not in your ad, not in your company’s tweet, not on your company’s Facebook page.
Unless you’re actually the United State Olympic Committee or an official sponsor, just stay a million miles away from all the words and all the symbols. If you’re Wham-O® don’t make a pretend symbol out of five Hula Hoops®.
And don’t even think about trying to use or register a trademark that includes the word OLYMPIC, unless you want to join the almost 500 other applicants who now have dead applications as a reward for their attempt.
How fast will your application die? Fast. Sarah Elizabeth Mason filed to register NERD OLYMPICS on May 4 of this year. She expressly abandoned that application before the month was out: May 31. Didn’t even live long enough to be rejected by an examiner.
An application to register Music Olympics was filed on July 25. That might live a little longer, but only because all of the lawyers are busy going after misuse of their trademarks in social media.
So, Just Don’t Do It.