I can't tell from the pictures how much, but if the rounding of the back side is not overly large then it will still work fine. A lot of them tend to get that way over time any way.
A goosewing can still work with a slightly rounded back -less than 1/16" or maybe 3/32" I'd say.
What I would recommend if you wished to restore it to working condition is to take a slow belt sander with fine paper and sand on the flat side, essentially establishing a bevel on this side about 2 or 3 inches wide.
Goosewing axes typically do not have the slight curvature to the bit like broad axes have, so some times they even have a very slight rounding of the flat side on purpose, if used by someone used to broad axes.
