Нужен простой календарь с отмеченными датами

Hello.

You just need to add widget for «availability calendar» only (instead of booking form with calendar). In the WordPress > Appearance > Widgets page in «Booking Calendar» widget for the option «Show» set «Only availability calendar» instead of «booking form with calendar».

Or if you have inserted the Booking Calendar shortcode (and do not use widgets), then you just need to insert other shortcode: http://wpbookingcalendar.com/help/booking-calendar-shortcodes/#bookingcalendar

Kind Regards.