I would be careful with mutexes.
You can't avoid it sometimes for resource sharing
But depending on the task priorities which share the resource, you might get quickly into deadlocks if one gets hold of the item, and is switched out afterwards while still holding it.
If you run into issues, you might consider specifying its priority inheritance option
Or using the preemption threshold option for the threads (enabling it from ThreadX src options)
For such signalling / synchronizing, a semaphore is IMHO definitely more safe
Regards