Hi again Claire--so it's a vanity case, then!
I just checked in Laura Mueller's "Collector's Encyclopedia of Compacts" (both her book and Roselyn Gerson's are must-haves for compact info--you might even check your local library for them, as they're both well-regarded references).
Anyway--page 303 has a 1925 Ladies Home Journal ad for Tre Jur with a picture of three compacts, one of which is yours (the ad shows the interior). It was called "The Triple", and the picture on the box for yours, as well as on the case, was the company logo, according to Mueller known as the "Little One."
Mueller does have a Tre Jur vanity case from 1929 (ie later than yours) in her book, which she values at $125-150.
As I said before, though, book values aren't really all that meaningful, except for the help they can provide telling you if you have something super-special or not! It's more helpful to google "20s vanity case" and see what's out there and what collectors are actually paying for items similar to yours right now.