is it necessary to call pthread_mutex_destroy on a mutex?

From IEEE documentation which is the standard governing POSIX:

The pthread_mutex_destroy() function shall destroy the mutex object referenced by mutex; the mutex object becomes, in effect, uninitialized. An implementation may cause pthread_mutex_destroy() to set the object referenced by mutex to an invalid value. A destroyed mutex object can be reinitialized using pthread_mutex_init(); the results of otherwise referencing the object after it has been destroyed are undefined.

The documentation does not say you must call it. But it is a good practice to do so.
Calling this api will signal the POSIX library to release all the resources which were reserved for use of this particular mutex object during its initialization.
It is logical to assume mutex initialization does allocate/reserve some resources.

If someone provides you with a destroy function, then you are required to call it as the final action on that object before it goes out of scope.

On architectures and implementations where the API has no effect, this will be optimised away, however if the API changes in future to require cleaning up of internal state and your code does not call it, your code will now have a memory and/or resource leak.

So the simple answer is yes; you must call this API - and here's the thing - even if the API does nothing at the moment, because although the API itself is fixed forever into the future, the implementation behind the API is not.