From the pictures it looks to be in original as issued condition.
The trigger housing is of the stamped variety used in the 1944 Underwood rifles. There should be an ordinance bomb stamp on the bottom of the trigger guard, if it is an original Underwood there will be a "U" stamped somewhere on the housing.
The push button safety, mag release, barrel band/swivel are correct for that gun for that time. Rear sight is correct and should have an "S" or "NPM" stamped on the left side.
The data indicates that the gun should have a round bolt but the flat top bolt could correct as the switch came between 1943 and 1944. So an early 44 production could have the flat bolt. It should be marked with a stamped "U" or "WU".
The stock is correct and the stamp G.H.D. over the U.E.F., and the handguard looks to be correct also.
Overall it would seem to me that you have an original, as issued, non modified M1 carbine. That is to say, a very, very rare piece. As such it would command a premium here in the U.S. The reworked/modified Underwood sells for around $1,500 and up. Your rifle, if I am correct in my evaluation would probably easily fetch $2,000 or more.
Congratulations on a very rare and unique piece of history.