Allowing a “friend” class to access only some private members

I think you can use Attorney-Client here.

In your case example should be like this

class FooA
{
private:
    void Hello();
    void Hello2();
    void Hello3();
    int m_iData;

    friend class Client;
};

class Client
{
private:
   static void Hello(FooA& obj)
   {
      obj.Hello();
   }
   static void Hello2(FooA& obj)
   {
      obj.Hello2();
   }
   friend class FooB;
};

class FooB
{
    void fun()
    {
        FooA objA;
        Client::Hello(objA);  // right
        Client::Hello2(objA); // right
        //objA.Hello3() // compile error
        //ojbA.m_iData = 0; // compile error
    }
};

class FooC
{
    void fun()
    {
        /*FooA objA;
        objA.Hello()  // compile error
        objA.Hello2() // compile error
        objA.Hello3() // compile error
        ojbA.m_iData = 0; // compile error*/
    }
};