I'm assuming that glowing you're talking about it the bright part of the relic quest they are working on. There is no way to turn off the glow. If it's a piece of gear, you'd have to get the same piece in a non glowing fashion. If it's a weapon, then well you're outta luck unless you get 2 of the same weapon, one upgraded and one not and glamour it which can't be done for the relic weapons glow.

Personally I love the glow. Shame the Augmented Magiteck Rod doesn't glow and looks plain as hell. It's an eyesore to look at.