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You know that 祖父 is grandfather and 祖母 is grandmother. This is both combined. Is it some hybrid grandmapa monster you've created in your lab? Hardly, it just refers to your grandparents.
The reading comes from 祖父 and 祖母, which are exceptional readings on their own, so you'll need them in order to be able to read this one too.
My grandparents still see their pediatrician.