That plastic thing that the centaur is handing out is a pinworm checker for gyochu kensa, or pinworm exam.
The exam involves having a piece of sticky cellophane (pin teepu in Japanese) that is applied to the anus and then tested to see if it contains pinworm eggs.
Usually done annually each spring for school kids and infants.
笑い飯(Warai Meshi) is a Manzai comic duo consisting of Nishida Kouji and Nakanishi Tetsuo. They were known as "the uncrowned sovereigns" due to the fact that in the annual manzai championship 'M1 Grand Prix' they repeatedly came within an inch of becoming champions but then unfortunately missed out. In the 2010 championship (which was the final one, as this championship ended with the 2010 competition,) the duo introduced their joke material "Santaur," a combination of "Santa Claus" and "centaur," and finally achieved their dream of winning the competition. There are people who say that their victory was a gift from Santaur.
Ah, thanks for the background info. It's even better with a context, since now it looks like they're thinking "What the hell have we brought into the world?"