Gammas were actually mentioned in the novel before, when the original bodyguard team left for their vacation, but the manhwa adaption left it out.
You also have dominant alphas and dominant omegas in this universe, the easiest way to explain gammas would be: a superior form of betas.
Gammas are extremely rare and they are the least affected by pheromones, which makes them the perfect candidates working for dominant alphas, especially as bodyguards. Chase's original bodyguard team consisted of gammas.
But least affected by pheromones doesn't mean completly imune, so that's why they needed a break.
Is that important in any way for this story? It actually is for the Miller family, but isn't mentioned in this story. Spoiler
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One of Chase's grandparents was a gamma turned omega.
Turning a gamma is much more difficult, if they even survive it. It's a massive blow on their health, and that one even survived giving birth.
The grandparents story (is one of the darker of the author) doesn't have a happy ending, and it traumatized Ashley Miller (Chase's dominant alpha father) and is one of the main reason's ( the others are the too early manifestations and number of children) why the family/upbringing of the children is/was so messed up.
WAIT IT HAS A NOCEL????
Yes, the author (Zig) actually writes webnovels.
WHAT THE FUCK ARE GAMMAS