You can force the responder to pick dates in the future or in the past by enabling the Only allow times in the past? or Only allow times in the future? options. This way, you can ensure that responders do not accidentally schedule a meeting for a time in the past, or specify a past event as some time in the future.
Additionally, you can set a range of dates and times by enabling Min date and Max date, which can help ensure users set meetings during available hours.
Date picker styling options
The date and time menu is rendered from the native date time input of the responder's browser. Currently, there is no dropdown version.