Now that's a Deer Rifle!  That barrel-band is a good feature and will guard against the stock splitting in front and behind the magazine opening.  I would put a magazine cut-off back on it (now missing) to prevent possible roughness in cartridge feeding.  I wonder if the Krag barrel was replaced with a re-chambered 1903 Springfield barrel?  Something about the barrel contour suggests that possibility.  Another possibility is that a tapered collar was fitted to the barrel to smooth the transition from barrel to receiver diameter.