If I were to wear your grandfather's watch I'd get it serviced and replace that dial because it is a bad re-dial. That's not taking into account any sentimental attachment you might have for the watch as it is. It looks like someone created that dial in their back shed judging by the uneven placement of the plots around the perimeter (eg. between 12 and 1) and the IWC logo is incorrect and too large. Below are what the logos looked like over the years so you can see the correct styles and sizes relative to the dial. Chart from Vintage Caliber.
If you pop the caseback off and take a photo of the movement the calibre should be identifiable. If you prefer to change the dial you can probably source one off ebay, IWC forum or elsewhere.
