There is an endless supply of benches along Swiss hiking trails.
To humans, they're just benches. To dogs, they are trailside buffets.
As a general rule, I recommend an exhaustive search of the entire bench area for scraps of food. Statistically, the area below the bench offers the highest payoff.
Prior to engaging in a systematic search, it is best to divert your parents' attention. To this end, encourage them to sit on benches that offer scenic views, like this one outside of Stierva in Canton Graubünden.
It is no coincidence that my parents refer to me as a Hoover. Sometimes Dad calls me Herbert, or even Edgar.