From what I can see I believe you have a Mauser Model ES350B single shot .22 target rifle made in Germanyprior to WWII.
A buddy's father-in-law was in Germany when they surrendered and sent home 4 grates full of guns, swords and all kinds of other ''souvenirs'' he'd ''liberated''. Contrary to what some believe Hitler never disarmed the German population. Perhaps this is how your grandpa got it. The vets brought home all sorts of guns, not just military stuff.
OH BTW, from what I've seen on auction sites your rifle could be worth as much as $3000 to the right person. Depending on condition of course.