Clear your browser history!!! Deny, deny, deny.
Don't clear your browser history. Tell them you'll let them see your browser history when they have a warrant.
Why anyone would let an elder look at his browser history is beyond me.
Hypothetical:
Elder: "Can I see your browser history?"
Me: "Hell, no." (We say "hell" in Texas even in the congregation.)
Elder: "Why not?"
Me: "Because it's none of your business."
Elder: "What do you have to hide?"
Me: "I'm hiding nothing. I'm preserving my dignity and privacy. You're not the police."
Elder: "Well, it seems to me that if you had nothing to hide you wouldn't be objecting."
Me: "Okay, let's call the service desk and ask them if it's okay for an elder to demand to see someone's browsing history. Better yet, let's call my attorney."