All a suppressor is, in terms of travel is another firearm
it is treated roughly the same way, you just don't declare it separately, keep a copy of the stamp under your foam in the case, and pretend it's not even there.
If you traveled with one separately, meaning no rifle, it's supposed to be declared like a firearm. Otherwise just keep it in the case, say nothing and drive on. Lately they have been very good with our rifles, I travel with one every trip and I am 1K Premier flyer, never without a weapon. They are waking up and too busy to worry about it, Fill out you card, drop it off where ever the agent says, and don't sweat it. They are just another bag.