Back to the input collar.
Notice Tremec was nice enough to send you a new seal with your new input shaft and collar. Tremec was also very nice and covered the collar with a greasy film to prevent it from rusting. If you press the seal into the greasy collar, then the seal will not SEAL and your Chariot of Fire will mark its territory--as well as your clutch and then you will probably teach yourself (and your neighbors) new vocabulary words.
The red stuff around the outside of the seal is actually a glue that seals the outboard ring of the seal to the input shaft collar. The glue won't stick to grease--SO, you get to clean AGAIN!!!