That sucks, Ray.
Make sure you get a new seat out of them, certainly don't settle for anything less. I guarantee they had that seat off and found it difficult to put it back on. They then tried to use some tool or other to help lever it on, resulting in the seat being ripped.
Let the dealer know you are clear about the seat being in perfect condition before handing it over to him and that if he doesn't pay for it, you will be contacting Triumph and also publicly shaming them on the Triumph forums.
If you say to them, you know there was nothing wrong with the seat as you only fitted it the night before, they can't really argue.
I really hope that gets sorted (I feel guilty for helping you get it on).
Matt.