When your Chromecast with Google TV (HD) or Chromecast with Google TV (4K) tries to pair with your Chromecast Voice Remote, it actively scans for Bluetooth devices to pair with. If your remote doesn't pair, your Chromecast eventually stops scanning, and you need to reboot it.
When your Chromecast stops scanning for Bluetooth devices, it'll play the "restart needed" chime.
To reboot your Chromecast, unplug the power cable from the Chromecast wait 3 seconds insert the cable back into the Chromecast. Your TV will show these instructions visually: