I have the same gun as you and it had the exact same burrs as yours. I filed them down myself. The PC (Bubba) gunsmith who filed the forcing cone didn't bother to clean it up afterwards. Not that I care, as my gun is a race gun only, but if you bought yours thinking that it being a PC would give you something special......... You are in for a letdown.
My hammer pin wasn't square in the frame with the top right of the hammer hitting the frame. Had to fix that too.
Now, Carmonize the hammer, tune your action to around 6 lbs, do a proper chamfer on the cylinder, a f/o front sight and put on a set of big butts and you'll have a proper 627.