On an older house, we repair what can be saved before we talk about rebuilding. Most walls with worn joints still have good brick in them, and taking a sound wall down to relay it costs you more and loses the original work. Rebuilding a section makes sense when bricks are cracked through or the wall has moved, and I'll show you why before it goes on an estimate.
We take old mortar out by hand where a grinder could chip the brick. A mechanical grinder is fast, but it can knock the edges and corners off old brick, and that damage shows along every joint for the life of the wall. Hand raking takes longer, so it costs more in labor, and on old brick it's the trade-off I'd pick.
Any new brick we add is picked to match the old in size, color and how it's laid, so a repaired patch doesn't read as a patch from the street. That takes more looking than grabbing the closest brick at the yard, and it's the part of the job people notice most.
Restoration sometimes turns up work next to it. An old fireplace with a crumbling firebox may be better replaced than patched again, and our fireplace installation work covers that. Where a plain block or concrete wall sits beside your restored brick, stone veneer installation can give it a finished face, and we quote that separately so you can decide on its own merits.