Thank you for the attached project. Indeed, there are styles in the Outlook skin, which interfere with the Special Day style that you have set. However, this is not a bug.
I recommend that you set a CssClass to the special days and override the skin styles like this:
itemDay.ItemStyle.CssClass = "lightBlue";
itemDay2.ItemStyle.CssClass = "lightBlue";
.TableLayout_Outlook td.lightBlue ,
.TableLayout_Outlook td.lightBlue a
Let us know if you need further advice.
the Telerik team