The Collaborative International Dictionary of English v.0.48:
Gantlet \Gant"let\, n. [Gantlet is corrupted fr. gantlope;
gantlope is for gatelope, Sw. gatlopp, orig., a running down
a lane; gata street, lane + lopp course, career, akin to
l["o]pa to run. See Gate a way, and Leap.]
A military punishment formerly in use, wherein the offender
was made to run between two files of men facing one another,
who struck him as he passed.
[1913 Webster]
To run the gantlet, to suffer the punishment of the
gantlet; hence, to go through the ordeal of severe
criticism or controversy, or ill-treatment at many hands.
[1913 Webster]
Winthrop ran the gantlet of daily slights.
--Palfrey.
[1913 Webster]
Note: Written also, but less properly, gauntlet.
[1913 Webster]