What could be behind it, or how could it be interpreted?
Since there is no scientific evidence for this particular practice, we can only speculate about what interpretations or popular beliefs might have led to it:

Aromatherapy and Indoor Climate:

Oranges: Citrus fruits in general, and oranges in particular, are known for their essential oils, which are released when heated. The scent of oranges often has a mood-enhancing, stress-reducing effect and can enhance the feeling of freshness and cleanliness in a room.
Salt: Salt can bind moisture. When heated, it could slightly contribute to the ionization of the air (similar to salt crystal lamps, whose effectiveness is also controversial) or simply serve to prolong or enhance the orange scent.

Health: A pleasant indoor climate and a scent perceived as calming can indirectly contribute to well-being and reduce stress, which can have a positive effect on overall health. However, it is not a direct cure for disease.
Folk medicine and traditional rituals:

In many cultures, fruits and spices are heated in various ways to release vapors or aromas that are said to provide relief from respiratory problems (e.g., colds). For example, onions or garlic are often heated.
Salt is used in many spiritual traditions to purify rooms or ward off negative energies. This could be a symbolic component.
It could be a very specific regional tradition, perhaps from areas with a similar climate to Ternopil, that has a specific meaning that is unfamiliar to us today.
The “money-saving” component:

This could mean that the remedy is seen as a form of preventative care, eliminating the need to visit the doctor or buy expensive medications by promoting general well-being. It could also be an indication that it serves as an alternative to commercial air fresheners or room fragrances.
In summary:

Although the idea is charming and can spread a pleasant aroma throughout the home, there is no scientific evidence or recognized medical studies confirming that heating a salted orange on the stove offers direct health benefits or can cure any illness. It is most likely a folk remedy or ritual whose effects are more likely due to aromatherapy, well-being, or psychological effects (belief in the method).

If you want to try this “secret” to spread a pleasant fragrance throughout your home, there’s nothing wrong with it. It’s harmless and can improve the indoor climate. However, always seek the advice of a medical professional if you have any health problems or illnesses.

Do you perhaps know the source or context in which this “doctor” shared this secret? That might provide further clues