Teepe Pillar is the attention-grabbing granite molar just east of the Glencoe Spire.
(So technically, it may not be a route on the Grand but a separate little peak, but listing it as a route will make it easier to find and produce more well-deserved attention.)
The Teepe Pillar (often spelled 'Teepee') is not named for it's shape (in which case 'teepee' would be the correct spelling), but for Theodore Teepe who slid to his death on the Teepe Glacier (immediately north of the pillar) in the early days of Teton mountaineering. I hope that makes him feel better about the whole thing.
The summit is surprisingly airy for something so dwarfed by the Grand, and you can test whether exposure really doesn't bother you by leaning over the sheer north face which drops 1,200' straight down to the Teepe Glacier.
Hike to the Middle Teton Glacier moraine and immediately go north to the Exxum Guide camp on a ridge below the east face of the pillar.
If you prefer the hard way, hike all the way to the shoulder between the Middle and the Grand, then descend along the black dike through the Glencoe Col to the base of the west face. Don't forget to add some rocks to your pack for even more difficulty.
Teepe Pillar offers several enjoyable routes to the tip.
The west face is an easy, straightforward 5.4 with four pitches and easy-to-find belays (just look for thick clumps of webbing anchors left over the years). This is also the exit route.
The east face offers at least three routes which may vary from 5.6 to 5.9, and if you don't have a better guidebook than I had, you might end up doing parts of all three.
Standard Teton rack. Nuts and a few hexes.