I'm not an expert in the period, and perhaps someone else can chime in a bit. But your question got me curious and the trope of the masked burglar appears to go back to at least 1852.

Well, I'm sure that the idea of a thieves concealing their faces goes back a lot farther. But that particular kind of mask is also called a "domino mask" and is associated with the traditional Carnival masks of Venice. I found this reference in a Wilkie Collins novel, Mr. Wray's Cash-box, Or, The Mask and the Mystery, pp. 84-85, in which a young man is being instructed by an old criminal in how to commit a burglary: "'Take your swag quiet, and you takes it safe...Fust [sic] and foremost, you've got your mask' (here he pulled out a shabby domino mask.) 'weary good, nobody can swear to you in that.'"

I also found a mention in this book that "burglar films" were practically a genre of their own for a while during the silent film era. Couldn't find any stills of any of the films he mentions, but I wonder if maybe this particular image of a burglar didn't get cemented then? Like take this scene in A Christmas Story --- the movie itself was shot in the 1970s, but in the memoir it's based on the author is talking about his childhood in the 1930s, and the scene is a pastiche of old cowboy and short film tropes of that era. This is speculation on my part but perhaps someone with better knowledge might chime in --- but in the context of say a silent film, where you need to quickly (and silently) communicate to the audience that a character is up to no good, having him wear a mask would be an effective symbol, calling back to the "masked burglar" idea that the Collins novel mentions, but having a domino mask in particular would still let the actor do reaction shots and be expressive.

I am not 100% sure what you mean, but criminals have often been depicted in popular culture with eye masks such as these. This surely resembles a raccoon.