I know Erasmus is joking, so we can assume that syphilis/pox was not ever really called the garden gout... right?
Apparently 'garden gout' is actually short for Covent Garden gout, because of the district's association with prostitution;
Harris's List of Covent Garden Ladies - Wikipedia
en.wikipedia.org
Erasmus wouldn't have used this phrase, it must have been a choice made by the English translator.