Calorie debt is when you are using more calories than you are eating and making up the difference from stored reserves of body fat.
Sometimes people will do this to save on the amount of weight carried and then replenish when back at civilization.
What are some good foods for recovering from calorie debt?
Even if it's only for a day or so, you'll need to rebuild your glycogen stores (though many light packable foods are starchy and will top these up quite nicely). That requires carbohydrates, including simple sugars (and not just one type as there are different receptors). Fat stores will also need to be rebuilt, especially over longer periods, but burning glycogen can lead to significant weight loss (as it's accompanied by quite a lot of water in storage); this can make it look like more fat has been burnt than is really the case.*
There's quite a lot of medical literature on this sort of topic; one example I've been reading recently† is Restoration of Muscle Glycogen and Functional Capacity: Role of Post-Exercise Carbohydrate and Protein Co-Ingestion. The title of that paper makes it clear that (in addition to many and varied carbs) protein is required, and in general difference macronutrients are processed through different pathways so a range allows the body to absorb more energy more quickly. That would be particularly important if you've only got a day or two before moving on again.
There's always the factor that sheer quantity is important, and both availability and palatability may not be what you'd like. Sugary drinks are an effective way to increase calorie consumption when you feel full or don't feel like eating large portions. Fatty foods are energy-rich, but they're rather satiating under normal circumstances (which appears to be less of an issue when severely depleted‡). They may however be a good way to end a meal if you find them tempting, even if you feel full easily.
In general, avoiding foods that are very high in water content and fibre is a good idea. This isn't the time for soup or salad. When trying to get patient's weights back up hospitals have guidelines that include "full cream milk", "extra nutritious snacks (e.g. cheese and biscuits)", and "add grated cheese". It's not in the source I've linked, but I've also seen recommendations to add extra-rich custard.
If you're only in a town for a few hours, but you know resupply options are good, you can get a head start by consuming some reserve food an hour or two before arriving in town. This assumes you have reserve food that's not being kept strictly for emergency use.
* To the extent that after a hard ride on a hot day people told me I'd lost weight since the previous evening, despite plenty of food and drink.
† This was in relation to some rather tough (for me) distance cycling over 3 days, and is covered in a question at bicycles.se, though with a different emphasis.
‡ The Minnestoa Starvation Experiment during late WWII looked at the effects of prolonged calorie restriction on otherwise healthy individuals. We can't assume that the results of this study apply directly to a calorie debt built up over days rather than months, but they found that during the recovery phase normal satiety cues were suppressed, a conclusion that many of us can agree with after prolonged exercise significantly in excess of calorie intake. Other studies also report that bingeing follows prolonged food shortages.
Don't overthink this problem!
I have decades of experience being in calorie debt every year, for two or so weeks at a time, at least twice a year, on backpacking trips (when younger), and I advise recovering from calorie debt by eating whatever you want, plus, at dinner, a glass or two of wine. But, even if you are ravenous when you get out, don't stuff yourself; you want your digestive system well rested and ready for a good next meal.
If you are healthy, and if you feel well after being in calorie deficit for 2 weeks or so, your body will tell you what it needs, through what it craves. And if that is an enormous salad, that is what you should eat, even if it doesn't have many calories.
I don't know what to suggest if you are not feeling well (that is, more than just feeling hungry), or if you are not in good health. Maybe chicken soup? In any case, the objective is to feel well, unless you feel bad enough to see a doctor, and forget about calories, regaining weight, and getting to your pre-trek belt hole.
The human body has millennia of experience of being hungry for some time, and then gorging on a mammoth, so it can certainly deal with 3 weeks of calorie deficit followed by a large meal. Although, with refrigeration, we do not need to gorge.
When you are on a hypocaloric diet for several days/weeks and you lose some weight, you do not need to call this calorie debt, especially if your new weight is closer to your normal weight than before. If you want to regain weight, you just need to eat some normal caloric foods.
There is no need to avoid "diluted" foods, like soups or vegetables, which are a source of water and fiber, both of which can help prevent constipation.
There is no need to stuff yourself with calorie dense foods, such as cheese, cakes, sugary drinks and meat - this will only make you feel bad. If you became underweight after a hypocaloric diet, hunger itself will make you eat more of - normal food. There is usually no hurry to regain weight because "caloric debt" after hiking is (usually) not a medical condition.
To prevent glycogen depletion (an immediate source of glucose in your liver and muscles) during a hike, you may need to consume quite some carbohydrates (maybe ~300 g/day), otherwise you may feel weak.
For optimal training performance, muscle glycogen stores must be replenished on a daily basis. For the average endurance athlete, a daily carbohydrate consumption of 500 to 600g is required (Sports Medicine).
When your glycogen stores are depleted, you will be in ketosis (increased levels of ketone bodies in your blood), which will give your breath and urine acetone or fruit odor. Your glycogen stores should be replenished in a couple of days by eating usual food; you can speed up this process by consuming more carbohydrates (~300 g/day).
