[LunarBerry]

hmm we've always had grazing dogs, especially our past yorkies. So far as I know Kimchi almost never grazes but we treat her to greens as we have with our past furbabies to reduce their grazing modes.
What we basically do is feed them lettuce or leafy greens (like romaine, spinach, etc.), mostly. They love the crunch bases of the lettuce. We find that when we give them greens, they seem less inclined to want to eat the grass as much. But of course, if they prefer the taste of grass, then there's not much else for it but you may try getting that pet "grass" that they normally sell for cats (wheatgrass). We also tried this method with some good results as well, we just hadn't kept up with it ^^;;