What motivates the stranger to ask Elisa about her chrysanthemums?

The stranger is a tinker: someone who travels from place to place, mending metal objects such as pots and pans. As part of his job, he effectively has to sell his skills to the people he meets on his travels, and like any good salesman, he needs to be able to service his potential customers' needs if he's going to make that sale.
The tinker shrewdly senses that Elisa must be very proud of her chrysanthemums. He sees this as a way in—something to exploit as part of his sales strategy. By praising Elisa's beautiful flowers, he's making her more amenable to a sale. If a salesperson can make a potential client feel good about themselves, then that will always make their job a whole lot easier.
And so it proves here. The tinker spins Elisa an elaborate yarn about needing some flowers to give to a lady friend of his. But, as Elisa discovers later, this is just a big fat lie. The tinker only wanted to get his hands on an old pot to mend, the pot he used to contain the bunch of chrysanthemums generously given to him by Elisa. But much to Elisa's sadness, the bunch of chrysanthemums ends up lying discarded by the side of the road. The tinker didn't really care about the flowers at all; he simply wanted to make a sale.