Chisel around the thin brick you want to replace by using your smallest mason's bolster. Scrape out crumbling mortar with a work glove, and then chisel again. Chip out a line of mortar around the brick. Be careful not to damage the bricks in the vicinity of your work.
Switch to a larger mason's bolster, and use it to remove as much mortar from the cavity as you can remove.
Pull the brick gently from the cavity. If it won't come out, continue to chisel the mortar until you can remove the brick.
Measure the depth of the removed thin brick. Take the brick to a brick veneer supplier, and find the brick's replacement by matching its depth and color to the supplier's brick veneer.
Mix mortar in a bucket according to the mortar manufacturer's instructions.
Scoop mortar onto a trowel, and fill the sides and the back of the brick veneer cavity with the mortar.
Insert the replacement thin brick in the cavity, and press it into the wall until the mortar squeezes out the sides. Use the trowel to scrape off the excess mortar.