"Hmm..."  Homura pondered the ghost's testimony.  Strange, possibly spectral woman.  Disappearances.  There were some options there, at least for narrowing it down.  "What did this phantom woman look like?  She wasn't super tall and wearing a big hat and white dress, was she?"  That'd rule out at least one spooky thing she read about on the internet.  

"Really, anything identifying will help.  Unusual hair or eyes, clothing, whatever you can remember about her."  Even if it turned out this phantom wasn't the culprit herself, she was a person of interest and possibly another witness.  Something had to have spirited the child away.  

Though speaking of, if children were being taken, they had to be taken somewhere.  That meant there would be some sort of lair to track down once they've got the target in mind.  Especially if there was any chance for rescue.  Hopefully it wouldn't involve some sort of spirit barrier or other little alcove carved out of the spirit world.  

"Forgive me if I'm completely wrong with this one," Homura started a suggestion to Shuichiro.  "But I don't suppose you'd be able to sniff out any trails left by spirits in the area?  Might be a way to track down this mystery woman."