Hi, And welcome to the forum...
Looks like it could be all matching and in original finish. If you haven't already, please check to make sure that it isn't loaded.
Would be a good idea to at least get it oiled with corrosion preventive gun oil (something like RemOil or a Hoppes product - you can find it at WalMart). Dont let the oil soak into the grips.
It's hard to judge things from your photos. Take some pictures outdoors and in indirect light (shade) without the flash. Get the entire side of both sides, and closeups on the markings.
You'll find disassembly instructions on this site. Be very careful removing the grips, especially the left one.
Does the magazine match the pistol's serial number? Get a picture of the base and any other markings
Value range could be $1000 (if non-matching or refinished) to $2000 (all matching with magazine matching with a high percentage of original finish).
Don't worry about the red oxide. It can be gently removed with well oiled "0000" or finer steel wool or bronze wool.
Check to see if your grandfather also had papers from his officer that authorized him to return to the US with his war prize.
Your pistol was made by Mauser in 1936. The entire serial number (including a letter suffix) will be on the front of the frame above the trigger guard. "1956?"
Marc
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 Igitur si vis pacem, para bellum -
- Therefore if you want peace, prepare for war.
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