Okay, this is a question that always gets me a bit riled up because the book version is so different from the movies. In Cressida Cowell's original series, the 'dragonmark' or the 'httyd infection' isn't really a medical condition you 'treat' with a potion. It's a mystical, psychological bond that forms between Hiccup and the dragon Furious, later Toothless. The mark appears on Hiccup's chest after he looks into the dragon's eye, and it's described as a sort of dragon empathy—he starts to understand them, feel their emotions, and even pick up some of their instincts.
There's no simple cure because it's not a disease; it's a transformation of identity. The 'treatment' is the entire journey of the last few books. Hiccup has to navigate being pulled between his human nature and this burgeoning dragon consciousness. He doesn't take medicine; he undergoes trials, makes huge moral choices, and ultimately achieves a kind of integration. The mark fades or transforms only when he fully accepts his dual role as the bridge between species. It's cured through character growth, not chemistry. The books frame it more as a destiny or a curse that becomes a gift, which I think is way more interesting than a plot device needing an antidote.
Honestly, I prefer this ambiguous, mythological approach. It gives the story its haunting, epic quality.