If you don’t want to show any dates with the timeline story, then you can remove the value of the date-format attribute from the shortcode and keep that attribute empty. This way, it will not show any dates on the story. However, adding custom text instead of the dates is not available in the free version of the plugin.
This setting is not in the plugin, but you can add custom CSS to disable this behavior if you want. You can place this custom CSS in the styles settings tab’s custom style editor section.