yes, ideally they should drill out the inclusion, unless it is larger than the drill hole or the cap - with the design of your loops there is no cap which would make it harder to conceal, so to have the remains of an inclusion showing where the single gold pin enters the pearl would not be so good, as it would likely show, as the pearls hang. An alternative with this design would be to hide the inclusion at the back, as the pearls hang, so you would never see it when the pearls are worn
re your photos, probably the veritical shot was taken in 'landscape', so you would need to rotate it one quarter turn clockwise on your PC, prior to posting, for it to show as 'portrait'
but Syd, your pearls and earrings look absolutely stunning - definitely one of a kind - the design is amazing
have you contacted the vendor to ask their views on the quality, colour, and setting of the pearls - that might be a start to helping you feel more satisfied, or on making the heart wrenching decison to return them ?