Looks like your event consumables (burgers and shakes) just get added to your inventory. I was hoping for a way to transfer them to the next event, but it was not to be. I have a few burgers in my present box that I'm going to leave them for Shards if it survives. These days, events can be really short, so you never know. Worst case, it'll come in handy for EG.

With the return of the Peroburger, we might consider the possibility that they're adding a different dedicated consumable for each event. So Peroshake/Peroburger for Gambit, Raw Pudding/Peronami for Shards, and something new (or just the standard pudding/peronami) for Elite Guard. I do recall that I got very little raw pudding and raw peronami in the last EG.