What is the manufacturer of a 308 Sniper Rifle known as a Kate?

Answer 1

Short answer is Remington.

But it is a mix of parts. The action is that of a Remington 700.

http://en.wikipedia.org/wiki/M24_Sniper_Weapon_System

The above is the Army sniper rifle. Gibbs used the Marine m40. In the episode you're referring to, the rifle Ari used was a Bravo 51, chambered in .308 Lapua. This rifle doesn't exist.

There is a Bravo 51, but it is chambered in .338 Lapua. There is no .308 Lapua. The Bravo 51 is named "Kate" and the rifle is only available in .338 Lapua. This platform is available in other calibers, but have different names.

The TV show mixed stuff, but it's just a show.