What I have understood from your Question is You want to add/delete menu items (placed inside the masterpage) through an control event placed in a content page. You can achieve the same through ajax also as you have asked.
Try as below .
Masterpage :
Step 1 : Place the Menu Control inside a separate UpdatePanel .
Step 2 : Add Public method for Adding or Deleting the Menu Items.
Something like
public void AddMenu()
{
MenuItem item = new MenuItem("NewOne", "NewOne");
Menu1.Items.Add(item);
}
ContentPage
Step 3: Place your repeater inside an update panel ( You have already done it )
Step 4 : Access the Public method
protected void CheckBox1_CheckedChanged(object sender, EventArgs e)
{
((SiteMaster)this.Page.Master).AddMenu();
}
Hope this helps