Removes Everyone including Inherited Everyone

Remove_EVERYONE+Inherited.ps1

# run as admin
# USE WITH CAUTION and test for desired results
gci -Recurse -Directory | %{
    $Descriptor = Get-Acl $_.FullName
    # first look for inherited access to we can disable inheritance and copy the AuthorizationRuleCollection 
    $InheritedAccess2Remove = $Descriptor.Access | ?{$_.IdentityReference -eq 'Everyone' -and $_.IsInherited -eq $true} 
    if($InheritedAccess2Remove){
        $Descriptor.SetAccessRuleProtection($True, $True)
        Set-Acl -Path $_.FullName -AclObject $Descriptor 
    }
    # now remove all explicitly defined access including what we converted above
    $Descriptor = Get-Acl $_.FullName
    $Access2Remove = $Descriptor.Access | ?{$_.IdentityReference -eq 'Everyone' -and $_.IsInherited -eq $false} 
    if($Access2Remove){
        $Descriptor.RemoveAccessRule($Access2Remove)    
        Set-Acl -Path $_.FullName -AclObject $Descriptor 
    }

}