I don't think the buggers do much to healthy mature plants, but I don't know for sure. I do, from experience, know that they can raise hell with seedlings though. They actually defeated one grow I did. I gave up, trashed the whole thing and started over.
In another grow they showed up in smaller numbers and I controlled them successfully by top watering with nutes infused with mosquito bits, so I think your tea bag is a great idea.
Good luck with it.