Does tresslers make you turn in your old starter to a vehicle when you buy one of theirs?

Some parts are exchange, some are not. Call them.

I've never paid a core charge there for any of the parts that I purchased. And they always have good prices on all the parts that I have bought from them.

I'm not sure about that part specifically but some you do Exchange

There may be a core charge for the value of the scrap material but if you want to keep your old one it would not cost that much.

I don't think you do