Although covered, the gap isn't necessarily filled with mortar. They'd have to use a jointer for that. And with a crack width of quarter of an inch, that may be difficult to do.
So to fill the crack, I thought of using a sealant. Of course, you'd need a sealant that's appropriate for masonry. But before that, clean the inside the crack with an old screwdriver. Remove any loose debris in there like soil. In our case, there were even remnants from the aerial roots from our old creeping ivy.
Apply the sealant into the crack with a caulking gun. Work from bottom up. Insert the nozzle of the caulking gun into the crack and apply pressure that will fill the space with sealant. Ensure enough sealant is applied with some excess protruding on the wall surface. Avoid wastage of sealant material as discussed in this entry.
Apply the sealant in spurts as you work your way upwards. When finished, you would have ribbon-like sealant material forming on the wall surface as shown below.
Flatten the sealant material by running your index finger along the crack starting from the bottom so you'd get a smoother finish. This also pushes the sealant further inside the crack.
In the process of running your index finger on the sealant, some gaps on the sealant may be created. Re-caulk these gaps or holes with the same sealant and run your finger again. After smoothing out the sealant, the sealed crack should look something as shown below.
Let the sealant dry thoroughly. You'd notice that the sealant though gray-colored doesn't have that typical concrete color. Actually, we could've used any sealant color because there is a way of blending the sealant color with the surrounding wall. See how that can be done in this entry.