My copy is well-thumbed; no mention of scopes being sold in the 1930s that I can recall. Do you have a reference?

It's really a shame the US didn't do better for scopes in both wars and Korea: B&L had a fairly close relationship with Zeiss until the USAicon entered WWI and afterwards they produced good stuff. It wasn't like the basic design of a good straight tube scope was any great mystery, nor protected by patents etc. Noske was producing a good product that could have been brought up to milspec, and of course the Lymans could easily have been improved as well.
"In 1921, the Small Arms Commitee ordered that all SMLE rifles be sent to Weedon for parts cannibalisation and scrapping. It is recorded that 9,788 of these rifles were stripped, their telescopes and mounts removed. Many sighs were sold surplus and adopted for sporting rifles; these may be encoutnered with range drums re-graduated for another cartridge."

On the same page Skennertonicon writes:

"Because the SMLE sniper rifle had all been broken up after the Great War, assorted sights from store were reconditioned and fitted to the No. 3 Mk 1* rifles by Alexander Martin in Glasgow, Scotland. These became known as the Rifle No. 3 Mk 1* T(A), the 'A' suffix indicating 'Aldis'

Quotes are from Skennerton, Britishicon Empire Sniper Rifles (Small Arms Identification Series No. 22), page 13.

You're quite right in that a nation with over a century and a half experience with scoped rifles did so poorly in WW II. The USMC was broke and pressed the Winchester A5/Lyman 5A into service along with some Unertls. Fear of the return spring catching in the brush meant they were removed, requiring the user to pull the scope back for a follow up shot; unnecessary movement kills. The Army liked the Lyman Alaskan better but the Weaver 330 was available and adopted solely on that basis. Lyman weren't plentiful enough. Concur that the Noske was a better scope and came in 4X (hooray for Noske in San Pablo) and at one point it was proposed that the USMC adopt it. They didn't (as we know).

The War Department adopted the W&S pre WW I but were not the first to issue scoped rifles. The Confederacy did that with the Davidson scoped equipped British Whitworth.

My information hows the PE being adopted in 1932-3, not 1931. It was not out in time for the film. I don't see why Timoshenko couldn't have the prop department make fake scopes. Turning a lathe isn't that hard.

It was from WW I and the dovetail cut into the receiver for the front scope base was filled. It was afterwards reproofed.