Storm, that's the same method I used for the checkering. Citristrip on heavy, let it sit a couple of hours, nylon brush took it down to the wood in no time.
Mine was a Remington 700 ADL with pressed checkering. Though the wood showed some rough spots where the checkering was pressed in, the stripper got ever speck of old varnish out of it. It did a wonderful job, clean as a whistle with no sign of anything being driven deeper into the wood -- whatever that might mean. A dozen or so coats of Lin-Speed, some rottenstone and it looks great now.