No remove button in sight. Dragging to trash does not work either. Trying to remove the item highlighted.
The trick with iTunes is that you don't directly manage files on the device, you manage them on your desktop, and choose what is synced.
Normally, iTunes syncs your entire library, only avoiding this when your device is full, or when you manually choose what to sync.
Your question is a tad ambiguous, so I'm going to give two answers.
If you want to remove a song from iTunes outright, deleting it from your computer and your synced devices, you must remove it from the "upper" Music selection, not the one listed under "On your device". The "on your device" list is read only.
If you want to keep songs on your computer but only sync certain ones, open the summary view on your iPod, select the "Sync" menu, and hit the "Selected playlists..." option. You can then create a playlist of the songs you wish to sync, and only sync that list.