I looks like it's a genuine article.  It seems to have at least one of the original rawhide ties, too.  The legend inside side is, I think, correct for the a U.S. action cover, but I don't know how you can confirm it is for a Krag.  I don't know how many model rifles they were intended for other than the Krag, but it would be logical to have made the same or similar design for a 1903, if they, indeed, did such a thing.  The Rock Island mark confirms it for the U.S. and that Arsenal was making Krag leather cartridge boxes for the Krag that could have also been early issues for the 1903.

The Enfield rifles also had a similar cover in use during the same and a little later period, but the wording for the cover placement was, I think, a little different and it closes with snaps rather than rawhide.

As to value, I paid $15 for one about 25 years ago and I have seen them listed since (2015) for $95.  The only one I have seen actually sell at auction was in 2011 for $75.  Todays values will probably be lower.