German WWII Wehrmacht Helmet?

hand painting helmets in basic camo patterns was pretty common on both sides during the war,

the dirty yellow type shade on the helmet is certainly real, there are plenty of photos around of germans in southern Italy and Sicily with similar shades of dark dull yellow hand painted on their helmets which was quite effective camo in the dusty and dry areas of the south or italy and Sicily and also a similar shade to the types of bricks used in italian buildings.

at a guess i'd suggest the black 'graffiti' on it was probably painted on by some bored allied soldier or Italian civilian who recovered the helmet from where ever it was dropped before your granddad came along and took it home with him, the inverted stripe you see on the front isn't a rank showing, that rank was for a senior private/lance corporal, your owner was a senior sergent, and the germans wore small rank patch's on their arms never their helmets, (that was an american thing)

in addition to that i'm pretty sure no german painted it for the simple reason the swastika is the wrong way round.

never the less, as already stated above you have a piece of rare unique history, don't paint over it, every dent, dink and scratch tells of story.

DO NOT, I repeat, DO NOT paint this helmet. It is an antique and could be worth a lot of money, but if you alter it in any way you could destroy it's value to a collector. I highly suggest that before you do anything at all to it that you take it to the appropriate expert and get his opinion of what needs to be done to it. The chips and dings in it shouldn't diminish the value of it at all, in fact they may increase it.

The flag of Imperial Germany had black, white and pink horizontal stripes (inspired via the black and white of the Prussian kingdom, and the pink and white of the Hanseatic League). The badge on the German helmet become probable presented in the time of WWI (whilst the Stahlhelm become presented, changing the older Pickelhaube helmet), yet retained in WWII. (nonetheless the Nazi swastika flag extensively utilized black, white and pink.)