Assuming the photo is fairly representative of the entire firebox, what's it going to take to repair all of the mortar joints in terms of time/cost? The width at the back is 24, the front is 30, and the height of the area needing repair is 30.
When dry skin is the cause of an itching back, it is easily remedied by applying a lotion or cream to moisturize the area. When chronic dryness and itchiness is an issue, a person may need to increase hydration efforts.
There are other causes of skin itching that are important. Common ones include thyroid problems (specifically hypothyroid -- which also gives constipation, feeling cold, tired), liver problems (sometime with yellowing of the skin). Dry skin is the most common cause -- in which the skin is scaly and falls off.