The Things We Hold On To (持つべきものは Motsubeki Mono Wa) is the first special episode of the anime series, and is considered as the eleventh-and-a-half episode.
It is an OVA bundled with the third volume of the manga: a fanservice episode at a swimming pool.
The Lost White "Earring" That Was On The Lady's Ear case
Eru, Satoshi and Mayaka come to the pool where Houtarou was working. After having some fun, Eru notices that a woman in a red swimsuit had something on her ear but later it is missing. Mayaka suggests that it was an earring or a stud that might have fallen off.
They come to the conclusion that if anyone accidentally steps on it they might get hurt. So the three of them ask Houtarou for his help.
After searching for it almost everywhere, Houtarou realizes something and asks Satoshi to hold Mayaka in his arms. Mayaka stars to go but then backs away saying it didn't matter who was holding her but because it was embarassing as she would "look like a kid". Finally she agrees to do it if Eru holds her.
This proves Houtarou's theory that when you hold someone in your arms the person will most probably keep their hands on the holder's shoulders. It is revealed that the "white earring" was actually ice cream that the lady's son was eating. She didn't know it was there and it got washed away when she went swimming in the pool.
Satisfied, the three of them go home, leaving Houtatou behind to do his work.
In the episode, Eru told Houtarou that he was special to her.