Final answer:
The woman's mitral valve disease is most likely caused by Rheumatic heart disease, which results from an autoimmune response to untreated streptococcal infections like sore throat during childhood.
Step-by-step explanation:
The most likely cause of mitral valve disease in a 54-year-old woman who grew up in a remote village without access to medical clinics and had several episodes of sore throat as a child is Rheumatic heart disease. Rheumatic fever, typically following a sore throat caused by Streptococcus pyogenes, can lead to rheumatic heart disease where the heart valves, particularly the mitral valve, are damaged due to inflammation (carditis).
This valve damage can later manifest as mitral regurgitation, a type of valvular insufficiency, where the valve does not close properly causing blood to flow backward and can lead to heart murmurs detectable via stethoscope.