There is a way to password-protect specific pages on a site. The first step is to upgrade to the Pro package so your account will have the Accounts module. (You can see all of the benefits and pricing for our package subscriptions here: https://www.gutensite.com/Website-Packages-and-Pricing#compare_pricing). (Religious organizations get a $10/month discount.)
With the Accounts module enabled, there's an option to make a page secure via the Page Settings options. By default, all pages are Public. Basic access simply requires a login to the site.
But, there are also Security Access Levels as well:
So, you can have finer control over who sees which pages, depending on which Access Keys are granted to their account.