Pie crust.
No, really.
Double-crusted pie was how late medieval Europeans "packaged" street food to go. This was convenient for the purchasers and eaters, of course. But we know from court records that it held some extra possibilities for especially...ambitious...sellers.
In 1351 London, Henry de Passelewe sold two chicken pies to Henry Pecche and his friends. Ravenously hungry, Pecche was halfway through the first pie when he realized the meat was rotten. The group of friends then opened up the second pie: also rotten.
They claimed to the court that Passelewe had deliberately sold them bad, life-threatening meat that was "an abomination to mankind--to the scandal, contempt, and disgrace of all the city!"^1
The court called in several other cooks and food-sellers in London to testify--per frequent medieval practice, based on Passelewe's fama rather than an ability to examine the relevant pies for themselves. A fiction writer might make up an interesting backstory for Passelewe here, because they witnesses easily concluded that the chicken had indeed been unmistakably rotten when it was into the pies. He had deliberately used the "container" as a disguise for his fraud.
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^1 Another, similar cased used the phrasing, "abominable to the human race, to the scandal and opprobrium of the City and the manifest danger of the plaintiļ¬ and his friends." This appears to have been rote legal language in English court records, which is why the Middle Ages are the best ages.
Along with the pie crusts, there's some textual evidence for disposable and biodegradable methods of takeout. Catullus (84-54 BC) described the writings of another historian as "only fit for wrapping up mackerel".
In Mamluk territory through northern Africa and the Middle East in the medieval period, most urban dwellers lacked a kitchen and would need to buy food from commercial sellers, such as mashed fava beans known in Egypt as ful medames or grain and rice porridges. These were sold in inexpensive clay containers that were rarely washed before being reused; more gruesomely, cracks could be repaired with congealed blood, which is both disgusting and haram under Islamic law.