I mean, you also have to be careful to return pointers and not smart pointers and so on. It can be a bunch of work if you need to write a bunch of freestanding functions to wrap the c++ object methods.
Well, you won't return smart pointers if your header file is in fact a C API, since smart pointers are C++ only.
It's usually as simple as calling data() on a vector or std::string (as well as having a function to return the length or size of the data buffer). And if you wrap your header file in the normal C externs, it shouldn't compile if you do things that are not allowed in C, if I remember.
But you are right it can be a lot of work if you have a large surface area. I try to stick to tight, focused APIs, and data is normal C structs which work fine in C++ as well.