What do I do about the pigeon?

His tapping seems most persistent.

Why not try opening the WINDOW?

Does he seem to be carrying something on his back?

He'd have to sit still for you to see what it is.

It seems impossible to catch him, though.

Look at the MAGAZINES on the bedside table for a subtle hint.

Try and catch the pigeon not where he is now, but where he is flying to.

Watch him for a while to map his movements.

His route is: windowsill -> headboard -> lamp -> chair -> bed -> cover -> picture frame.

While the pigeon is ON THE MOVE, tap on his NEXT stop in order to catch him.

Tap him in your inventory for a closeup.

After reading your message, set him free. Be kind to animals.

Drag the pigeon to the window to let him go.