The only thing I can think of is when we can get the chip for that one lady that demands trophies as proof, you get the chip, turn into the museum, check in with the curator, then take the chip back and turn into the quest giver.
I've also been wondering if there's no other way to get it. It does kinda feel like a genuine JPRG mechanic, but I've also always felt like it's a jackass thing for devs to do.