The Player's Manual contains explicit rules on food / water consumption that you will want to refer to.
A character needs a pound of food a day and can make the food last longer by subsisting with a half-ration. Eating half a pound of food a day equals half a day without food.
A character can stay without food for a number of days equal to 3 + his Constitution modifier (minimum 1). At the end of each day beyond this limit, a character automatically undergoes a level of exhaustion.
A normal meal day resets the number of days without food.
A character needs a gallon of water a day or two gallons a day when it is hot. A character who drinks only half of that amount of water must make a DC 15 save save or be exhausted by the end of the day. A character having access to even less water automatically undergoes a level of exhaustion at the end of the day.
If the character already has one or more levels of exhaustion, it takes two levels in both cases.
–Food and water, Player's Manual, p. 185
An alchemy pitcher is more than capable of producing a gallon a day (up to 8, in fact, fresh water), and there is no rule that fluids produced by the pitcher of alchemy disappear with time, so in a temperate climate, an alchemy pitcher could produce enough water to feed 8 humanoids, which means that the excess can be spent on the food.
A humanoid must consume at least 1 pound of food to stay fed, and an alchemy jug is capable of producing 1 gallon of honey, 2 gallons of mayonnaise, 4 gallons of beer and 1 gallon of wine. The 5th edition D & D does not have rules concerning the balancing of macronutrients. Therefore, at least, according to the rules of the game, 2 gallons of mayonnaise (or about 16 pounds) is enough to support up to 16 creatures a day.
Realistically, a group of up to 5 characters could survive on a pot of alchemy, producing water 2 days out of 3 (5 × 3 = 15 gallons of 16 gallons produced) and producing Mayonnaise every third days (5 × 3 = 15 pounds of 16 pounds produced), with an excess of 1 gallon of water and 1 pound of mayonnaise every three days.
So, unless the party is bigger than 5 humanoid creatures, there is no need to call for any type of control in the first place. They are perfectly capable of feeding themselves and being watered.
I mean, you have to take the Jug Alchemy Jug if you intend to run a real survival campaign.
Although we believe that only water feeds and that surviving in honey / mayonnaise / beer / wine does not provide enough nutritional value to survive (which, if you're running a survival campaign, is not unreasonable applies), water is easily the most difficult substance to obtain. Literally, the real-world professional survival guides emphasize the second priority, the safety of water, which comes after the protection of predators and elements. And in game mechanics, spending a single day without water (or even with poor quality water) is much more challenging than spending days without food.
Thus, an article whose sole purpose can only be to trivialize this part of the difficulty will always be a problem, regardless of the players' attempts to also let this article meet their dietary needs.
So, if you intend to properly restore the survivability mechanisms of your campaign, you will have to delete this item. Talk to your players, explain the problem to them (and make sure you play the same game), then, after doing all that and getting your players' consent, give you a narrative justification to explain why the pitcher has disappeared. Does not work anymore.