Are you saying dirty dishes would remain fermenting on the train until the next time that trainset passed through the same station? That sounds pretty unsanitary, and the insides of those warming boxes would get mighty skanky.
As you do in any catering operation, anything left on the plates gets scraped off and thrown into composting/trash. That is serviced as any other trash/recycling on the train. The plates with some things left on them get thrown back in the box, which itself is cleaned between jobs.
Whether or not you have one vendor servicing contained segments is another matter for the tender.