Don't know if this is new but I just checked and you can set your diet preferences in the account settings.
I hardly believe restaurants prepare extra food in advance just to sell it a huge discount with very little or no profit. Actually whenever I went to a restaurant that participated it wasn't leftover stuff but they cooked the meal fresh just for me. I guess they're using the app as a way to advertise and draw more people in with a big discount and hope they come back again to eat there at the full price.
There is a filter in the settings for vegan/vegetarian. In my experience the shops/restaurants always asked me if I eat meat/fish when filling the bag, but I also live in a very hipster area where it feels like majority of people is vegan now, might be different elsewhere. :)