Chris: Congratulations on being given a family Parker. Do you know if it has been in the family from the start??
The gun looks well used for sure. It should be a 12 gauge with 30 inch Damascus barrels. If the barrels are 30 inches, then it probably has not been intentionally altered, just well used. The capped pistol grip butt stock is correct for the serial number. There are wear issues with the wood, which could be repaired. At least one of the trigger plate screws looks like a non standard replacement. Some screws have had the slots damaged. Correct replacement screws are available and would need final fitting. The barrels look dented here and there in the pictures but that could be lighting effects. Barrels are the most important feature of the gun if you are wanting to shoot it. Folks on the forum can fill you in on Parker knowledgeable gunsmiths closest to wherever you live. If the barrels are salvageable and you are a shooter, it might be nice to pull it all together and think of your grandfather while enjoying the gun. If you do not want to shoot the gun, you may want to leave it as it was given you or you may want to do cosmetic clean up for display. The unwritten rule of thumb is do the "least harm" possible when doing anything. Many a potentially decent gun has been really damaged by good intentioned clean ups.
Folks here are happy to share knowledge and opinions, so feel free to ask a lot of questions before doing anything or having anything done to your grandfather's gun. I would consider a long time family gun to be priceless, regardless of grade, and a bit of a treasure to keep in the family for generations to come.
Cheers,
Jack
This was my father's gun. The wood was in similar condition to your grandfather's gun. I was able to clean it up and it turned out pretty well.