This method is letting in non-Letters instead of throwing an exception.

public class Order {
  private String itemName;
  private int priceInCents;
  private String discountCode;

    private String normalizeDiscountCode(String discountedCode)
    {
      boolean isLetter = true;
      char[] chars = discountedCode.toCharArray();
      for(char c : chars)
      {
        if(!Character.isLetter(c))
        {
           isLetter = false;
        } 

      }
      if (isLetter == false)
      {
        throw new IllegalArgumentException("Invalid discount code.");
      }
      return discountedCode.toUpperCase();
    }

    public Order(String itemName, int priceInCents) {
    this.itemName = itemName;
    this.priceInCents = priceInCents;
  }

  public String getItemName() {
    return itemName;
  }

  public int getPriceInCents() {
    return priceInCents;
  }

  public String getDiscountCode() {
    return discountCode;
  }

  public void applyDiscountCode(String discountCode) {

    try {

      this.discountCode = normalizeDiscountCode(discountCode);

    } catch (IllegalArgumentException iae) {

      System.out.println(iae.getMessage());  
    }



  }
}

public class Example {

  public static void main(String[] args) {
    // This is here just for example use cases.

    Order order = new Order(
            "Yoda PEZ Dispenser",
            600);

    // These are valid.  They are letters and the $ character only
    order.applyDiscountCode("abc");
    order.getDiscountCode(); // ABC

    order.applyDiscountCode("$ale");
    order.getDiscountCode(); // $ALE


    try {
      // This will throw an exception because it contains numbers
      order.applyDiscountCode("ABC123");
    } catch (IllegalArgumentException iae) {
      System.out.println(iae.getMessage());  // Prints "Invalid discount code"
    }
    try {
      // This will throw as well, because it contains a symbol.
      order.applyDiscountCode("w@w");
    }catch (IllegalArgumentException iae) {
      System.out.println(iae.getMessage());  // Prints "Invalid discount code"
    }

  }
}