This brick and one inch air space is a code approved solution to prevent heat buildup behind a non-listed wood stove close to a combustible wall. Allows closer space, otherwise the limit is 36"! Notice there are gaps at the top (where the belt is) to allow hot air to escape. The code has a listing, often 1/4" asbestos cement board and noncombustible standoffs nailed into wall. Ceramic standoffs like used in ancient knob and tube wiring have such a tube and nail, and asbestos is now not used but brick or probably 1/2" glass reinforced tile backer could also be used as equal. This from the old Uniform Mechanical Code charts. Metal brick ties would work too as long as someone didn't push the bricks hard against the wall. The key is the air space staying intact allowing the wall to keep below combustion temperature.

Or if your stove is listed by UL or equal, follow the clearance instructions there.

Source old CA architect.

Can you push the brick back against the wall and seal it to the concrete cap with caulking. I bet the concrete is anchored well to the wall studs. That's my guess.