If you caught any Greco-Roman wrestling at the Olympics, you might have been perplexed that stuffed animals kept finding their way onto the mat. They weren't being thrown by overzealous fans and it isn't some weird tradition in Greco-Roman wrestling akin to Detroit Red Wings fans throwing an octopus onto the rink during games. The stuffed animal is actually being thrown by coaches who are calling for a challenge.
For a coach to call for a challenge, the rulebook states, "The coach must request the challenge by throwing a soft object on the mat, immediately after the refereeing body has awarded or failed to award points to the contested situation. If the wrestler disagrees with the coach’s decision, the sponge is returned and the match continues."
The rules on what the "soft object" is are a bit vague. Standard matches have coaches throwing something like a spongey brick into the ring, but taking a page from Hollywood, the Olympics are taking the opportunity for what amounts to a little product placement. The stuffed animal is Vinicius, the Rio Olympics' official mascot.