The DnD world supports examples of various curses.
So your Tiefling could have came across a cursed artifact (either by stealing it, or receiving it, knowingly or not, as stolen property). It could have been a necklace, ring, knife, etc. Upon touching the object, it changed their skin tone as a punishment (to mark them as a thief).
Because the magic used has an anti-dispel effect, this is an in-game mechanic that would justify why it can't be easily removed: and thus why the tieflings skin color remains changed.
The game mechanics also support giving your character physical traits as part of a backstory. The official Basic Rules on Personality and Background states the following:
You choose your character’s age and the color of his or her hair, eyes, and skin. To add a touch of distinctiveness, you might want to give your character an unusual or memorable physical characteristic, such as a scar, a limp, or a tattoo.
So, explaining that your character is the victim of a purely cosmetic curse is legitimate, especially as it doesn't affect the core game mechanics.