The delete icon is not supported in the CssOnly mode. It is replaced by more universal system of "active areas". You can add the delete button using BeforeEventRender:
protected void DayPilotCalendar1_BeforeEventRender(object sender, BeforeEventRenderEventArgs e)
{
e.Areas.Add(new Area().Right(3).Top(3).Width(15).Height(15).CssClass("event_action_delete").JavaScript("dpc1.eventDeleteCallBack(e);"));
}
Don't forget to include areas.css from Themes directory.
<link type="text/css" href='Themes/areas.css' rel="stylesheet" />