I don't really care. I rarely look at the thanks/groans I get; thanks are nice, keep those, but the groans don't bother me if I get them. I like Evince's scheme of limits and selling them, but what's the currency? bitcoins? could get complicated...
I do rarely groan people; it is a way to tell them their post is stupid/awful/whatever without having to comment in the thread. (very useful if one is banned from the thread).
The only abuser of them that I know of is Legion Troll; and if he couldn't groan what would he do all day? But if there's a way to stop one user from hitting the groans button, stopping him would take care of the abuse.
Maybe we should start an educational campaign....
"Groan Abuse - next on Oprah!" "Save the Groan button - keep it from being abused!" "SPCG - Society for the Prevention of Cruelty to Groans". "Hitting the Groan button makes hair grow on your hands!" "Groans: not just for breakfast anymore." oh wait, that last one won't work...
Keep them, toss them, I don't care. Now I'll go vote that way.