Eliminating unused local area network icon
I have a laptop that I use exclusively with my wireless network at home. I have the wireless network icon in the lower right corner of my screen with the green broadcast signal showing a connection.
I had to do some phone tech support troubleshooting yesterday, and they had me plug in the laptop directly to the modem. Now I have this Local Area Network Unplugged icon (2 monitors with a red X between them) on all the time in the lower right corner of the screen.
Question: How can I delete the icon, without eliminating the possible need to "plug in" to the network again in the future?
Should I go to Control Panel / Network Connections, and delete (or disable) the icon there? Will that delete the software so I can't connect in the future?
Thanks