The GG grips themselves are pretty tough for normal usage, but I would advise against looping a thin guy around them... I bet it would cut/saw into the grip in windy conditions and end up damaging them.
That said, I can think of two viable alternatives:
1. Not sure about the LT3s, but my LT4s have a little cord loop below the grip (no wrist bands, just this little orange cord loop). You could probably loop a guy through there, to get the correct height for the pole.
2. If you flip the poles the other way up (grip on the ground) and position them a few inches away from the tarp, then loop the guy around the tip, resting on the basket, then to ground a few feet away. This would mean that the area where you tie the guy to the pole would be a few inches above the tarp, but your guy would go UP to it, around the pole a couple of times, then down. I bet that method would work. Might want to put a ziplock or a little piece of material under the grip to ensure that it doesn't get too muddy or whatever!