You can remove that message. However due to the way this has been designed it may be a little complicated in your case. The switch for this is embedded in the home page slide show preferences. The slide show preferences are only available once you have uploaded one or more photos to your site. Here's how ...
Upload one or more photos to your family tree. Then, when signed in as administrator, select the Home Page option under Home in the top menu. In the top left you will see a link to "edit slideshow". Click the link. You will see options to disable the "recent events" section.