DocM, we were in the same situation, saving extra bricks from our home construction and then using them to build our pizza oven/outdoor fireplace. We opted to mortar-in just the holes of the corner bricks. We didn’t see any need to fill in the holes of the other bricks. If I can figure out how to attach it, I’ll include a photo of our oven. While we may still add some adornments and maybe cover the bare concrete sides, the oven itself has been in use since November 2018 and performing well. No problems with the bricks whatsoever. Buona fortuna!