As I can’t say whether or not this one came with those grips, they were offered from the factory with them, usually on the stainless/nickel (idk what finish that is, assuming it’s stainless), with a gold trigger.
" With the exception of special order nickel-plated units and the above-mentioned versions, all of the 1931 Baby Browning pistols were finished in chemical hot blue. The halt to exports to the US in 1968 was mandated by the Gun Control Act of 1968 - which was precipitated by Robert Kennedy's assassination involving an Iver Johnson manufactured revolver."
That case itself is collectible to some.
I bought a used Ruger Mk1 in the late 80s and it came in a Browning case like that, just a little bigger.
Browning Hi Powers came in cases like it, I believe in the 1960s.
I was looking on GB the other day and such a case brought $100.