Removing web sites from safari 11.0.3 activity bar

How do I remove a website from within the Safari activity bar on my desktop iMac? I have tried everything - clearing history, under privacy, clearing all website data, etc. and yet I still have a website that I cannot remove no matter what I do. I have turned on cookies turned off cookies, rebooted everything, I have run disk first aid, etc., etc. I have even deleted all Safari data from the Applications Folder and emptied the cache. When the main apple Safari browser opens, on the top left side of the activity (pages open) bar, right under the red window close button is a web site icon. I wish I could say it doesn't bother me but it does and I want it gone. I don't want someone riding my web life. Like I said, I have tried everything I can try - except - reloading the entire OS X El Capitan 10.11.6 software. I'm willing to do that if it will go away but my fear is that my information is going to be retained by this blood sucking unwanted guest. Any ideas that you can provide me with would be extremely helpful. I actually have another identicle iMac desktop computer that is just sitting in storage. Should I just get that one hooked up and simply bring my important files over onto it from the one that cannot shake the hitchhiker? Or will all info still be attached to my various web related sites? I realize that I have posted this same issue previously and then dropped the ball with all of you that helped and I'm sorry for that. I've always appreciated the help I've received on these forums and hopefully someday, I can help someone else.

HELP!!!