The Remington finish is tough to get off. I have used epoxy paint stripper with good sucess. I believe it is a Jasco product. Spread it on and let set until it bubbles up, then scrape it off with a craft stick or something that won't scratch the wood. If your workplace is cold it will take longer to bubble. You might have to do this a couple of times. Work stripper into the checkering and clean out with a stiff plastic brush. This stuff is not good for you so do it in a well ventilate area and wear some old gloves. If it gets on your skin you will feel it.
Then I sanded lightly and applied Tru-Oil. No stain is needed to duplicate the factory finish. Takes several coats of oil to fill the pores and make a nice finish. Apply oil to the checkering only on the last coat, worked in sparingly with an old toothbrush. Not difficult, but time consuming. Good luck.
Phil