What are the mouse badges for?

Question

I just started playing Professor Layton and the Last Specter (Specter's Call in the UK), and periodically I see a little mouse running around. If I tap it with the stylus, I get a mouse badge.

I'm up to four now and haven't found a use for them yet, although the game hints at there being one.

What are they for? Do I need to unlock something in the story before I can use them?

Answer 1

When you get 10 mouse badges you unlock minigame "Mouse Alley".

The maximum amount of mouse badges you can get is 99,but there are no other rewards for them other then minigame "Mouse Alley" at 10.

Sources: Source #1 Source #2

The badges are required to unlock the minigame, but there are a couple other requirements, too:

You have to solve the Luke Foretells mystery and talk to Fische at the Crossroads.