Translation:We do not want the meals on dirty plates.
In English you can eat a meal, you can have a meal, but you can't put a meal on a plate. You would never say, "put the meal on the plate". It would be nonsense, unless you were referring to cornmeal. I am happy to learn that jidla is distinct from jidlo in Czech but in English I think it's all food...
If we interpret this sentence as meaning, for example, we are in a cafeteria where plated meals are available at the counter, I can imagine someone saying, "We don't want the meals on dirty plates," when it is clear that some plates are cleaner than others. In general, "We don't want the food on dirty plates" could be used in a different sense, like meaning "We've heard about this place.... so when you bring us our food, make sure you put it on clean plates!" But I think "We don't want our meals..." could be used there as well.
And you can definitely put a meal on a plate. If you cook dinner for your family, you can either serve it "family style" or plate each meal individually. In the first case, you put out large plates and bowls, each containing all of the food of one type, and then everyone takes what s/he wants individually. In the second, you load each plate yourself, putting the complete meal, for example, a piece of chicken, a baked potato, and some broccoli, on a plate for each person. Both methods are commonly used, at least in the US.
I disagree. Can you imagine saying, "I am putting your meal on a plate?" (Unless it is some sort of boxed "meal"like a happy meal or a premade commercial dinner). Otherwise, maybe in defiance of a fast -food mentality, you might insist that "We eat OUR meals on plates." At any rate, the Czech word jidla evokes "food" in English and we use "food" for the prepared items that go on plates. So I think that "food" fits for this situation. Also, the word "meal" is often meant for something broader than mere food, it is also an event, "the evening meal" for example. Does jidla carry that significance?
I do not trust this "dictionary". It uses automation and SEO techniques to appear at the top of the Google searches, but they never show the translation in the snippet so that you have to click and generate revenue.
Notice that even when they try to define it as "n pl" almost every single one of those automatically searched examples is actually genitive singular.
Anyway, I see "meals" and "foods" there.