Many types of problems with tefillin battim can be repaired:
Tefillin Battim Corner Repair
Broken Tefillin Battim
Gassos Tefillin Battim that have rounded or dented corners can usually be repaired:
I asked Rabbi Shraga Feivel Halevy Zimmerman how round a corner on tefillin battim has to be in order to require fixing. He explained that we simply don’t know how far we have to go when it comes to corners that are not perfectly square. It is not clear what the halacha demands from us and therefore “Anyone with a modicum of yiras shaymim should have all corners fixed that are not completely round”. This does not mean that if you see a tiny spot of paint missing that it needs to be fixed (assuming that they are still black). I will try to show you some pictures of corners that don’t need to be fixed as well as corners that need repair and what to expect them to look like after the repair.
Here are pictures of the same battim after the corners have been repaired and painted. This was a simple painting job with only one coat of paint and no sanding. In order to achieve the brushed look of new battim five coats of paint are required followed by careful finish sanding. As you can see, with repaired corners and a fresh coat of paint, these tefillin look great and I was able to keep the cost much lower than had there been five coats of paint and sanding.
Broken Tefillin Battim:
These tefillin battim broke in half. They are peshutos, and can be put back together. This is not a repair that could be done with gassos.