- I can not think of any official canon reason why Teal'c kept the brand of Apophis.
- Most Jaffa have the brand of their "oppression" fully visible and is a big part of what makes them who they are.
So first as I said there is no real official reason for it, but one can be relatively certain to why.
The "brand" as I will call it is something that most Jaffa have from very early age. It is a brand of their false-god signifying who their master is, what their allegiances must be, etc. without the need to utter a word. As Broklynite mentioned it can be related to the serial numbers inked onto Jewish prisoners during the second world war.
I believe the biggest reason Teal'c never would have gotten rid of it would have been to shove that very fact back into the face of any Goa'uld he faced from then on. Every time they see not only his shol'va face, but the fact that their "brand" is working in defiance of everything it stands for. A simple example would be someone drinking a nasty ol' Pepsi in a Coca-Cola ad; just pure utter disrespect!
Equally as big I think is that fact that his brand, however it may be perceived is a part of who he is. It represents not only the struggles he has had to overcome, but the link to Master Bra'tak, the respect he was able to earn over the years, and it is a bond that ties him to all other Jaffa.
I might also wonder if the Teal'c would have seen that as a slap in the face to the Sodan. Removing the brand might be perceived as an attempt to call himself a Sodan warrior, whom Teal'c has the utmost respect for, and he would not wish to be mistakenly "grouped" with those legendary warriors... As well as the Sodan might take offense to that themselves.
It also did come in handy with certain situations when his identity was not known or his betrayal had not reached that corner of the galaxy. One example is in Season 3, Episode 9 when SG-1 comes along a group of kids Apophis was training to infiltrate the SGC as SG-X. They did not know his true allegiance, but believed he was aligned with Apophis due to his brand.