Just got off the phone with AppleCare Assistance. Called them about a different problem I have been having (noted in this forum), and said "oh by the way". Donna at Apple Care discovered that this TL thing does NOT occur on my iPhone. So perhaps my iPhone is using something other than the wifi here in the building. We ended up blocking the Bing address that had been showing the unlocked warning on the computer, and re-entering. Now the padlock is there and the warning has disappeared. Apparently somehow my computer was tuning in to an outdated Bing address. Now sure how that was possible, but it seems to be working correctly now. Thank you all for your thoughts and suggestions! They helped immeasurably in me being able to explain to Apple Care what was/might be going on.