1956 New Zealand Threepence Strapless? Grade? Value?

Sure is!
A search on Google Images should confirm.

Mary Gillick is the die designer for the first type (series) of Elizabeth 11. The letters "MG" are to be found incuse on the truncation of the bust.

The master die of 1953 had to be re designed when it was thought that an implication could be drawn that the young Queen Bess may be in the nude, because on weakly struck coins, the shoulder strap could not be seen.
THAT would simply not do for our (then) young Queen Bess!
In addition, her ear was also rather weakly defined on weakly struck coins.

Actually, the bodice line on Bess's chest is clearly visible on ALL coins of Gillick design. As a woman, Mary G. would have already known this! I reckon that Mary G. may have known more about dress design than the preparation of working dies.
I would think it was a forgivable oversight, especially when mint technicians didn't spot the problem early enough either!

A new master die was prepared and was ready for use on the British coinage of 1954.

The later master die was progressively used for coinages of the British Commonwealth on and after 1954.

By 1956, all British Commonwealth coinages utilized the second master die, and that includes the 1956 New Zealand threepence.

Somehow, one of the original first design dies got used on some of the '56 N.Z. threepences and bronze pennies, I guess by mistake. No big deal at the time; the '56 strapless coins were issued along with the rest of the '56 issue, with the second design die.

The '56 strapless PENNY (estimate 50,000 minted), is scarcer then the '56 strapless threepence (estimate 300,000 minted, cat. value: N.Z.$450 in AU).
ref. The New Zealand Coin & Banknote Catalogue, 2010.

I do not know of a reason why the Cat. value is THAT high for the '56 strapless threepence, perhaps someone else in the CCF can explain this.