I can't imagine why you would want to do that? The only military cases I've ever used for accuracy loads have been match cases. I also have a bunch of pulled 5.56 military bullets around, but I never use them. 22 caliber bullets are just to cheap to warrent using military FMJ bullets. I have tried them with the thought of pelt saving bullets, they weren't all that hot. Out of a 223 I found a hot loaded 50 gr Hornady SX to be far superior in all way's.
If you do do it, use an inertial puller and slam it hard. Those bullets appear to be glued in, you'll see the glue ring on the bullet when you get it out. A press mounted puller will mar up the bullet badly. The powder you save, you can't properly identify so you won't be able to reproduce the load without pulling more bullert's and then the lot number will likely change so consistenty may go right out the window. Hint, the powder makes a good lawn fertilizer, just sprinkle it on the grass.