TW is Twin Cities Ordnance Plant. This would be Korean war era ammo. Probably corrosively primed, but that's not certain. Corrosive rifle primers were mostly phased out of American made military ammo by the end of 1953. That's not a big deal if the brass is not corroded. Having a look inside with a borescope to check for corrosion wouldn't be a bad idea if you happen to have one available, but a flashlight is good enough.
If it were mine, I would give the brass a wash in a quart of 10% citric acid (lemon juice is about 8% and is close enough, but more expensive) with a teaspoon of dishwashing liquid added, shaking it on and off for ten minutes, followed by a thorough rinse in tap water followed by a dip in acetone to remove the water, then allow it to dry. I would then anneal all the case necks just in case the brass had been exposed to airborne ammonia gas over time, leaving it prone to season cracking.
I know nothing about the shooting qualities of this particular brass, but see no reason it wouldn't be the same as most other military brass. That is to say, it should be about as good from an accuracy standpoint as, say, Remington brass, but will be a little hardier for use in the Garand. But it won't be up to Lapua.