Great question! Tea has a variety of minor health effects primarily due to the antioxidants and caffeine that it contains, but you asked specifically about the effect on the gastrointestinal tract. The caffeine will increase the body's secretion of stress hormones, which redirect blood from the gastrointestinal tract to the muscles. This will slow down absorption and possibly contribute to indigestion. Stress hormones will also increase the secretion of gastric acid which can also contribute to indigestion. However these effects are minor as long as you don't drink too much tea, and tea typically has less caffeine than coffee or soft drinks. Excessive consumption of hot beverages including tea could also slightly increase the risk of esophageal cancer.

Sources: http://en.wikipedia.org/wiki/Health_effects_of_tea
http://en.wikipedia.org/wiki/Health_effects_of_caffeine