The replies in this outside thread led me to discover that a cookie is indeed being set in the browser that instructs a Google translation to be applied. This is the information I was after.
edit: Specifically, the plugin displays the Google Language Bar on my site. When a visitor uses this language bar to switch the language of the page, a googtrans cookie is set on my page, corresponding to the indicated language (screenshot). As I understand, the cookie is added by an external script hosted by Google, not by the plugin. So I cannot delete the cookie, or cause it to expire.