Back in the late 80s/early 90s there was a kind of tie that men would wear with plaid flannel shirts. They were usually drab-colored and had a bumpy knitted texture to it. They didn’t taper off into a V-shape like most ties, but ended with a straight line, like: |_| They seemed less formal than regular ties.
That’s odd, because the standard definition of “rep tie” seems to be a woven silk necktie like this one: the sort of thing most people mean when they say “necktie”. “Rep” specifically refers to a weave pattern with longitudinal ribs, which would not apply to a knitted tie.
Seriously, although they were (and still would be) out of place with formal business attire, they went very well with casual plaid shirts, as mentioned in the OP.