How can I guide the rat to Calvin?

After you've exchanged messages with Warren and the paper stops working, send the rat into the vent and use the arrows to guide him around.

Guide the rat to the black square (exit to a lower level) on the bottom right.

Now you can't see the walls on the bottom level, but you can deduce them.

Go up, up, up, up, left, up, left, left, down, down, left, up, left, up, up, right, right, right, right, right, down.

But how to retrieve that grenade? Maybe if he could tie it to something so you can pull it back?

Tap the loose yarn on the jailbird tapestry to unravel it.

Tie the rat with it and send him back down the vent.

Pull the yarn to retrieve your grenade.