Well, this episode is basically about babysitting the little Febri. Since Uiharu can’t find any information on Febri’s identity and adding her into lost child database receives no response, most probably Febri is an Child Error. There are facilities to take care of Child Error. While waiting for a place to be prepared for Febri, the group decided to take care of Febri for 5 days.
The funniest part of this episode is how Febri is scared to Mikoto, and somehow very attached to Saten. And the desperate Mikoto is using her best shot to be liked, by using a Gekota finger-puppet. The result is… Febri takes the Gekota, still afraid to Mikoto, and Mikoto lost her complete collection of Gekota finger-puppets, lol.
At this point, I can guess that those mysterious guys with laptops who performed “experiment” on Mugino was a group of students. Students with extraordinary brain, but have no special esper power. Thus they are trying to prove that esper power is not everything and their inventions can actually be stronger than level 5 espers. But that’s just my speculation for now.