The mystery has been solved. I couldn't understand how some Zetas said that their badge was engraved. Mine literally has no place to engrave even initials.
I called the company and it turns out that the backs of the new badges (like mine) are different from the backs of the old ones. Mine is what's called a "crown" backing (appropriate for ZTA
wouldn't you say?!!) What that means is that it is in two tiers. The jeweled area has holes all around it so it lets the light in, and the enamel area is sunken in and covered by the clasp and pin.
The older badges had a solid back so there was plenty of room to engrave.