You can refresh your memory on YouTube. Saving Private Ryan is there in clips,and,I believe,the full movie.
I'm not a historical tech expert on the 1903A4,but I'll try for you.
The Army and the Marines had different versions of the bolt action Springfield sniper rifle.
Spielberg took some "poetic license" with the movie. The correct rifle for an Army sniper would be the 1903A4 equipped with the little 2 1/2 x 3/4 in diameter tube scope. While there MAY have been some minor variants,the common scope was the civilian Weaver 330,with a military designation of M-73(I believe)
That scope did all the work. It was NOT mechanically feasible to pop the little scope off and replace it with the long Lyman or Unertl target type scope as they did in the movie.(Which was used on Marine rifles in a 6X version)
That's just not accurate. For Hollywood,the big scope was "better drama" Maybe,but it compromised historical accuracy.
Late in WW2 they ordered some 1903A4 rifles equipped with the Lyman Alaskan 7/8 tube scope,also 2 1/2 X. It was a better scope,but the war ended and the order was canceled.
I'm sketchy on this next part,but I believe the basic Lyman Alaskan was given a facelift with a sunshade and turret covers ,etc to become the scope you have on your Garand. Production went to some outfit with the word "Ford" in the name,...but lets not call that historical fact. Its an "As I recall"