She first contemplates that the birthmark may be dangerous to remove because trying to do so may lead to a cureless deformity. The birth mark here is used as a symbol of human imperfection, and this phrase may mean that humans are meant to be imperfect and therefore trying to remove the imperfection will only lead to more imperfection (cureless deformity).
It may be necessary to note that the story was written at a time when religion still played a major part of people. In the western world where the author lived, Christianity was the major religion. From a biblical point of view, imperfection was also regarded as a positive thing because it is the only thing that separates mortals from God. By accepting that humans are imperfect, they are then allowed to recognize that God is above them. However, refusing to admit their imperfection amounts to pride that is regarded as blasphemy (incurable deformity) and thus leads to a sin that is not forgivable (incurable deformity).
The second part of the phrase is also significant. In this part, she says, “or it may be the stain that goes as deep as life itself.” In other words, the only way human imperfection can be removed is by death. This has two significant meanings. first that for human beings, perfection can only be achieved through and during death. Again, this concept has its roots in most religions and especially Christianity which advocates for the idea that it is only when people have died and their spirits gone to heaven that they can hope to be perfect. Although this sentence can also be regarded as a sign of what would happen later when they tried to remove the birthmark, that is, the death of Georgina after going through the “plastic surgery”, it may also mean that she was saying that if they become arrogant enough to want to correct what nature (God) has set, they must be prepared to face death.