Dana gives care to marnie's dog when dana finds marnie's dog ill on the side of the road. after marnie locates her dog, marnie promises to reimburse dana for the cost of treating the dog. marnie's promise is binding, because there is a bargained-for-exchange.

That statement is False.
the way for an agreement to be considered as 'binding' is if there is a written agreement that signed between all parties involved or if the agreement happened publicly in the eyes of many witnesses.
In the particular case above, Marnie could went away without paying the reimbursement and still facing no consequences.