Clear the mortar out of the damaged joints, starting the with horizontal joints. Pry the loose mortar out of the joints with a trowel or screwdriver, then dig into the remaining mortar around the damaged area with a carbide-tipped grout saw.
Go at least 3/4 inch into the joints.
Clean the joints with a stiff wire brush and a vacuum cleaner to remove any loose debris.
Spray the bricks around the damaged joints with a garden hose until they are soaked. The bricks will absorb the water, preventing them from soaking water out of the mortar as it cures, which can weaken it and cause it to crack.
Allow the bricks to dry overnight.
Prepare a batch of mortar according to the manufacturer's instructions.
Hose down the surface of the bricks again to make them damp.
Fill the horizontal joints with mortar, using the edge of the trowel to press the mortar in until each joint is completely filled. After the horizontal joints have been patched, fill the vertical joints with the mortar.
Run a joint tool over the surface of the mortar to create a curved edge in the mortar. If any mortar gets onto the brick face, scrape it away with the trowel before it hardens.
Wipe a brush diagonally across the joints after the mortar has become firm. This removes dry bits of mortar from the joints.
Spray the bricks and mortar lightly with water to make them damp. Cover the wall with a tarp for three days as the mortar sets.