The Tenri Grip is a unique way of gripping a lapel that is useful for throws like uchimata and harai-goshi. It is said to have originated at Tenri University, a top judo university in Japan. The Tenri Grip is particularly useful for Osoto-Gari in an Ai-Yotsu (same sided, e.g. right vs right) situation.
The gripping approach allows tori to bend uke's head and thus put him in an unbalanced situation -- an ideal situation for a throw. Osoto-Gari can be a dangerous throw because if you don't unbalance uke properly, he can easily counter you with Osoto-Gaeshi (basically Osoto-Gari you back). The Tenri Grip allows you to thwart such a counter.