I've never seen this, and I'm not sure I entirely understand your situation, but it sounds like you're getting reflected light off a green surface. All turf is at least a little bit shiny, so you might consider shooting with a polarizer filter to cut down the reflection. It's worth a try. The filter will cost you a stop of light, but it sounds like it only happens on sunny days, so you can probably afford that.
How far up does the green go? Is it limited to their legs, or does it green up chests and faces?