Judging by the picture, I am going to assume the rest of the stock is in the same condition.. I agree with C3 when he states to stay away from the sand paper... My suggestion is to use a stripper used for wood and remove the entire finish that is currently on the stock.. You may or may not need to stain it.. (glenfield stocks were not stained usually) depends on your preferences... Select your type of finish either tung oil or boiled lindseed oil (tung oil will be a better choice for moisture protection but has more gloss than BLO).. In either case, hand rub it in for best application..
One thing to remember is that your rifle came with a hardwood stock.. Nothing fancy like walnut etc so it's pretty much an open canvas. If you must "sand" on the wood to remove any hairs left from the stripping process, use 0000 steal wool to remove them.. (wood hairs is what I'm refering to).. Good luck. Lemme know if you need anymore help.. I've done many stock refinishing jobs over the years for myself and others.
For anyone wondering why I say to strip completely? You might just be amazed at how pretty the hardwood stocks are when you remove that factory spray on finish..