Though there was no naturally occurring cure, an anti-toxin was created by the Fourth Doctor using a bioanalyser in combination with a medikit. He successfully used this cure on Leela, against whom Calib had used a thorn. (TV: The Face of Evil)
Although the Doctor told her "No more Janis thorns... ever", (TV: The Face of Evil) Leela continued to use them on her travels with the Doctor, sometimes firing them through a blowpipe. In Victorian London, she used one to kill a Chinese assassin threatening the Doctor. (TV: The Talons of Weng-Chiang)
When The Master temporarily brainwashed Leela to believe that she was his assassin, she attacked the Doctor with a Janis thorn, but the Doctor was able to get to the TARDIS laboratory and retrieve his previously-prepared antidote, although he was so weakened by the poison that he had to convince Leela to inject him with the antidote because he couldn't do it himself (AUDIO: The Evil One).
The Seventh Doctor would later face the same issues of a companion carrying a dangerous item he disapproved of when Ace frequently created and smuggled Nitro-9 under his nose, which he obviously knew about. (TV: Silver Nemesis) However, in this case the Doctor was more willing to be lax about his disapproval, as the nitro-9 could be used for demolition purposes where Janis thorns could only be used to threaten human life.
Behind the scenes Edit
In early rehearsals for The Face of Evil, the word "Janis" was pronounced with the first syllable rhyming with "can". However, Tom Baker pointed out that "Janice Thorn" sounded like the name of an out-of-work soap actress, so the pronunciation was changed, rhyming the first syllable with "cane". (DCOM: The Face of Evil)