You did a good thing. Now, seal the checkering well to prevent moisture absorption. I use a high grade polyurethane, not less than four thin coats, to totally seal the open pores of the exposed wood. Minwax Marine satin does well for me.
Sealing checkering my way is time consuming but worth it to protect the stock and the checkering itself. The fragile wood diamonds will absorb enough of the plastic finish to become quite hard and stronger than it will otherwise be.
Before starting each coat, carefully rub a thin layer of paste wax around the pattern to assist cleaning off the inevitable build up of the poly over the existing finish. I use Kiwi neutral shoe wax, applied with a finger tip and a paint-thinner damped cleaning patch to carefully remove the stock over spread after each coat. Use a cheap, kids type, water-color brush to apply the polly.
Saturate the first thinned coat. Let it soak for five minutes or so and pat off the remaining surface liquid well. Allow the finish to fully cure, 4-5 days, until it is hard - and don't hurry this step! Then, lightly run over the checkering with your single line cutter again. (If it clogs, use lacquer thinner to clean the goo.) The cutter will "sand" off the numerous tiny burrs and greatly smooth the final product.
Repeat the polly coat, very thin, and brush away the excess finish with a toothbrush and carefully wiping away the stock over-lap. "Sanding" with your single line cutter may be needed again. Once more, allow it to harden until it's well cured, probably only two or three days this second time.
Repeat coating it until you can see that the wood is filled and sealed with as much finish as it will absorb. Curing time for thinned polly should only be a couple of days after the first two coats.
It is very important to keep each polly coat thinned and applied thin, mix it only a little thicker than water. Work to remove any excess, keep it well tooth-brushed out (after the first coat anyway) or a thick finish layer will clog your pretty work. But doing less than a complete sealing coat leaves the checkering to act as a wood sponge in rain, absorbing much more water than uncheckered bare wood would.
Enjoy!
You would do well to have the stock removed and also seal the raw wood inside the stock and under the butt plate while you are doing it. Again, avoid a thick build up on the surfaces.