Ok, trying to make some sense here, instead of the forgotten umbrella that became a youkai, it's the forgotten hankerchief?

Kogasa's hands are wet too. Maybe she stole it?

BadRoad said:
Kogasa's hands are wet too. Maybe she stole it?

My guess? The one she has in her mouth is hers to dry her wet hands. When she saw Sanae with wet hands and nothing to dry them she offered hers.