Yep. The grips that would be original to that gun would have diamonds around the screw holes, and sharp, "high horned" shoulders. It also looks like someone replaced the original "fishhook" hammer with a later target hammer.
These are really things that would only matter to a collector gun. That one should be a heck of a shooter, like the one I have, and will outlast you.
eta: here's a pic of one with the correct grips and hammer that I just grabbed. The hammer on yours could be original though. There are others here who can tell you a lot more about them than I can.