This link to the Parker Gun Collectors will take you step by step through removing the stock. Follow it exactly and youll be fine. For a lot more Parker information go to Parkerguns.org and click on their FAC section. Worlds of topics and how to stuff.
http://www.parkerguns.org/pages/faq/StockRemoval.htmI will add that Parker checkering was flat topped and should be kept that way. Just dont cut it too deep and youll be fine. Restoring the rounded mullered border is a bit more difficult. I used a very small rat tailed needle file to recut it on mine. And keep the two lines beside it very shallow with your single line cutter. You might find yourself using a small triangular needle file to work on these lines as they curve. I am pretty sure Parker cut the round portion of the border with a very small gouge.