Dependency Injection - service accessing the private members of the client

I have a client class A which has some data structure (m_data). Now I need a function which needs to perform some operations on the data. Is it a good practice to use the dependency injection, so the given service will access m_data of the client class?

Note: There are more service, they all operate on m_data, I would just like to avoid inheritance. The reason for that is that class A is also a derived class, so there might be other classes delivering the foo() functionality, but not the m_data data structure.

class B()
{
public:
    // constructor, destructor, ...
    void foo();
}

class Service()
{
public:
    // constructor, destructor, ...
    void foo(Data);
}

class A() : public Base
{
public:
    A(Service &_serv) :
        m_serv(_serv)
    {
        init_data();          // initializes m_data
    }

    void foo()
    {
        m_serv.foo(m_data)    // is this a good practice?
    }

private:
    Service m_serv;
    Data m_data;
}

I guess this is a bad practice, so could someone provide some good design patterns, or any other solutions? Thanks!