Why does this compiler warning only show for int but not for string? "type qualifiers ignored on function return type"

I am a bit confused about some warnings I get when compiling my C++11 code using mingw64. This is my MWE:

class A{
    const string name;
    const int ID;

    public:
        A(string name_, int ID_) : name(name_), ID(ID_){
            // initialize non-const members
        }
        const string getName() const{return name;}
        const int getID() const{return ID;}
};

int main()
{   
    A aObj = A("Aname", 1);
    std::cout << "getName() = " << aObj.getName() << std::endl;
    std::cout << "getID() = " << to_string(aObj.getID()) << std::endl;
}

Code executes fine and does what it should, but I get this compiler warning:

,,localtest.cpp:10:9: warning: type qualifiers ignored on function return type

[-Wignored-qualifiers] const int getID() const{return ID;}

So the warning only shows for getID() but not for getName(), even though both have the same type qualifiers. Can somebody explain to me, why this warning seems only to show for string but not for int? I suppose it has something to do with int being a primitive data type - but what exactly?

std::string is a class that has member functions that can be constant. If you have a constant object of the class you may apply only constant member functions.

As for fundamental types like for example int then the qualifier const does not make a sense for a return value because in any case you can not change the returned value.

Here is a demonstrative program

#include <iostream>
#include <string>

template <typename T>
const T f( const T &t )
{
    return t;
}

int main() 
{
    std::cout << f( std::string( "Hello World!" ) ).length() <<  '\n';

//  Invalid assignment  
//  f( 10 ) = 20;
    
    return 0;
}

The program output is

12

As you can see you can apply constant member functions to the returned object of the type std::string (but you can not apply non-constant member functions). And you can not change the returned value of the type int.