I am not sure if there are property settings for this but for our Windows Forms controls almost anything can be done with a DrawFilter or a CreationFilter.  Removing elements is one of the easier things you can do with a CreationFilter.  Here is some code that should do what you are looking for:

using System;
using System.Collections.Generic;
using System.Text;
using Infragistics.Win;
using Infragistics.Win.UltraWinSchedule.MonthViewSingle;
using Infragistics.Win.UltraWinSchedule;
using System.Drawing;

 class RemoveIconFilter : IUIElementCreationFilter
{
    #region IUIElementCreationFilter Members
    public void AfterCreateChildElements(UIElement parent)
    {
        if (parent is SingleDayAppointmentUIElement)
        {
            UIElement symbols = parent.GetDescendant(typeof(SymbolCharactersUIElement));
            UIElement text = parent.GetDescendant(typeof(EditorWithTextUIElement));
            Rectangle newbounds = new Rectangle(text.Rect.Location,new Size((symbols.Rect.Right - text.Rect.Left), text.Rect.Height));
            text.Rect = newbounds;
            parent.ChildElements.Remove(symbols);
        }
    }

    public bool BeforeCreateChildElements(UIElement parent)
    {
        return false;
    }
    #endregion
}

To hook this filter up to your MonthViewSingle do the following:

ultraMonthViewSingle1.CreationFilter = new RemoveIconFilter();

This was tested using the Office2007 ViewStyle.  It may need tweaking for what you are looking to exactly do. 

Here is a link to a Devin Rader's blog post that talks about a spy tool that is integral to writing these filters:

http://geekswithblogs.net/devin/archive/2005/11/17/60406.aspx

Help article that explains our Presentation Layer Framework with a link to Filters at the bottom:

http://help.infragistics.com/Help/NetAdvantage/NET/2008.1/CLR2.0/html/Win_Presentation_Layer_Framework_PLF.html

 You can find some samples regarding filters in our Knowledge Base:

Creation Filters:

http://devcenter.infragistics.com/Support/KnowledgeBaseResults.aspx?type=Full&query=(creationfilter+or+creation)&articletypes=0&age=0&sort=LastModifiedDate&samplesonly=0 

Draw Filters:

http://devcenter.infragistics.com/Support/KnowledgeBaseResults.aspx?type=Full&query=(drawfilter)&articletypes=0&age=0&sort=LastModifiedDate&samplesonly=0