Italian guanto, Spanish guante are likewise ultimately from Germanic. The spelling with -u- was established from 1500s.
military punishment in which offender runs between rows of men who beat him in passing, 1660s, earlier gantlope (1640s), from Swedish gatlopp “passageway,” from Old Swedish gata “lane” (see gate) + lopp “course,” related to löpa “to run” (see leap). Probably borrowed by English soldiers during Thirty Years’ War. Modern spelling, influenced by gauntlet (n.1), not fixed until mid-19c.
To issue a challenge: “The candidate flung down the gauntlet and challenged his opponent to a debate.” A gauntlet was a glove; the wearer would throw it to the ground to show that he was challenging an opponent to fight.
see run the gauntlet; throw down the gauntlet.