in practice, I do recommend recycling the vowels. Some new players can burn down the 2, 3, 4 piles and stall the game out. Having vowels always there helps prevent that. The desired behavior for the app is to just put the trashed vowels on the bottom of the pile.
After playing again, I had decided I liked what the app was doing and was going to play the card game similarly. Thanks for the clarification; I hadn't realized all the trashed vowels were going back into the supply (it's very difficult to tell until the stack has been exhausted). Anyway, it makes more sense than only recycling that last couple of them.