Don't forget the chocolate!
Syphilis is merely the most terrible of four related diseases: Syphilis, yaws, bejel, and pinta, caused by four subspecies of Treponema pallidum. Yaws is mostly tropical, and easily cured these days. Pinta is found mainly in South America and the Caribbean. Bejel is mainly found in the Middle East, and is somewhat a non-venereal syphilis that doesn't affect the brain. Yaws are thought to be the oldest (1.8 million years) form. Around 1415 Henry the Navigator, and his father and brothers, conquered Ceuta, in northern Morocco, which had long been a port filled with Barbary Pirates.
Even if syphilis and pinta were new world diseases only Columbus could have brought home, Henry was poking around hotbeds of yaws and bejel. (Trade with the Middle East had been going on for a long time by then, but Henry intensified exploration further south.)
If this circa 1415 skeleton really does have diagnostic lesions, they could have been caused by yaws, or less likely, by bejel. Voland's Right Hand suggests syphilis could have been mistaken for leprosy, which sounds reasonable. And Grikath makes sense in suggesting that while it was there before, sailors could have brought back a more potent form. If there are at least four flavors of the disease, there may well be local differences in virulence.
Those making politically-correct whinges about Columbus should remember that chocolate is a new-world food.