How can i remove/delete digits in the beginning of a string ?

You could just find the index of the dot and use the String.Substring method:

string s = "1. hello";
string t = s.Substring(s.IndexOf('.') + 1).Trim(); //= hello

private void FindRecursive(TreeNode treeNode)
        {
            foreach (TreeNode tn in treeNode.Nodes)
            {
                //tn.Text = "1. hello"
                string x = tn.Text.Substring(tn.Text.IndexOf('.') + 1).Trim(); //= hello
                if (x == this.txtNodeTextSearch.Text)
                    tn.BackColor = Color.Yellow;

                FindRecursive(tn);
            }
        }