Greenies would irritate a cat's digestive system... looking on my container for Greenies Pill pockets, "dried cultured skim milk is listed as an ingredient". I only used these because I had difficulty pilling Charlie back when he had stomach issues.I'm not sure about temptations, but I'm wary of Greenies treats because I've heard they can irritate some animals' digestive systems.
My cat wasn't interested in the first few freeze dried treats I tried, but she really likes the Orijen freeze dried treats, especially the Alberta boar ones. I also found Vital Essentials freeze dried minnows the other day, and she absolutely adores those.
I also like the idea of getting a really high quality kibble and using those as treats, because my cat really loved her dry food before I got her.