Why did the US have a law that prohibited misusing the Swiss coat of arms?

Question

From Reuters news on recently passed legislation (alongside the spending package):

those who misused certain emblems - the U.S. Forest Service’s “Smokey Bear” and “Woodsy Owl” characters, the Interior Department’s Golden Eagle insignia, the 4-H Club emblem, and the Swiss Confederation’s coat of arms - would no longer face jail time. People who use those symbols could still face civil lawsuits.

Why did the US have such a specific law regarding the Swiss Confederation’s coat of arms in the first place?

Apparently this prohibition was introduced (in 18 U.S. Code § 708) in 1948; the earlier versions seem to date to 1936 "Foreign Relations and Intercourse (June 20, 1936, ch. 635, §§ 1, 2, 49 Stat. 1557)" It's also distinct from prohibitions on misusing the Red Cross (which apparently are/were not repealed).

E.g., did the "Foreign Relations and Intercourse" act of 1936 prohibit misusing other coats of arms (or flags)?

Answer 1

I found historical diplomatic papers that may shed some light on this.

The Swiss Legation to the Department of State

On the other hand, attention should be called to the fact that in Article 28, Paragraph 1, of the Geneva Convention on the amelioration of the lot of the wounded and sick in armies in the field, of July 27, 1929, to which the United States became a party on August 4, 1932, it is provided that the Governments of the High Contracting Parties the legislation of which might not be adequate shall take or shall propose to their legislative bodies the measures necessary to prevent at all times “the use by individuals or corporations of the coat of arms of the Swiss Confederation or of signs constituting an imitation of it, either as a trade mark or for a purpose contrary to fairness in trade, or under conditions capable of wounding Swiss national feeling”.

The Swiss federal authorities would therefore be greatly pleased to see the United States adopt the law for the application of the Geneva Convention of July [Page 801] 27, 1929, contemplated in Article 28, Paragraph 1, of that Convention, or any other suitable measure.

Answer 2

It seems that this is about the Red Cross, and treaty obligations of the USA:

Art. 28. The Governments of the High Contracting Parties whose legislation is not at present adequate for the purpose, shall adopt or propose to their legislatures the measures necessary to prevent at all times: [...]

(b) By reason of the compliment paid to Switzerland by the adoption of the reversed Federal colours, the use by private individuals or associations, firms or companies of the arms of the Swiss Confederation or marks constituting an imitation [...]

So there is a treaty obligation to include this protection. It is rarely used. Apparently, there have been only been 4 references to it in Judicial opinion, two in error, one referring the historical context and one quip that the USC contains "ridiculously obscure" provisions such as this. Nobody has ever been prosecuted under this clause.