THE SIMPLE ANSWER: IN HIGH ELEVATION, YOU SHOULD ALWAYS BE PREPARED FOR UNEXPECTED WEATHER.
Here's the full question: "I am planning on a trek on the Teton crest trail and was wondering if thunderstorms in July and August in the high elevations are a problem in the Tetons. I have backpacked in August in the Colorado rockies and it was definitely a hazard there."
More specifically, here's what Grant Teton National Park (GTNP) Ranger Bobbie Tumolo had to say: "It is quite common for a passing afternoon thunderstorm to come through on any given day. They are usually quick though." She also threw in a bit of extra advice, "Also know that higher in elevation there, it is also quite possible for there to be a need for ice axes and crampons until mid-July. Not always, but also not uncommon. It's an incredible place!!"
If you ever have questions about weather, calling a ranger is one of the best ways to get the most accurate up-to-date info. I wrote about the Teton Crest Trail, where I included the GTNP contact information. Here it is for your convenience:
Craig Thomas Discovery and Visitor Center
I highly recommend calling them as you get closer to your start date. Rangers are awesome and can be so helpful!