It seems you're expecting yes or no answer, but it's not possible as different warts are caused by different factors (e.g. often by HPV and 35 other which can result in potassium deficiency) and it also should be not confused with moles which can look similar or some warts can turn into cancerous tumors.
Wart removal rarely involves anything more complicated than an at-home remedy and usually over-the-counter medicines can help (liquid, cream, or bandage forms) by applying them directly to the wart. Other traditional methods include freezing or placing a small piece of duct tape.
Though a potassium deficiency is not directly responsible for causing warts, it can be a contributing factor to outbreaks. So warts are the effects of being low in potassium, so it's likely that banana peels would help in this case as it's rich in potassium (as well as potato peels and Apple Cider Vinegar). And increasing your intake of potassium will limit the chances of your warts coming back. Bananas are considered safe to use as there are no side effects.
So I'd say it's worth to try.
- Warts at Natural Remedies
- Natural Cures for Warts - More Than Home Remedies
Warts & Moles at Herbal Legacy
Warts and moles are usually the result of a nutritional deficiency and they should be treated internally, as well as externally.
Potassium Deficiency for Warts and Moles: When cysts or tumors grow in places where they can be seen outside the body, often we react by having them cut out. This defeats healing by working on the effect instead of the cause. You can cut cysts out, tumors off, and burn warts off (which are also a potassium deficiency), or get rid of as many moles as you wish, but unless you go to the cause, they will grow back again, and you may end up with as many or more cysts, tumors, moles as before. Different signs of potassium deficiency will keep popping out on the body because the condition that needs correcting is on the inside. You have to go into the cause, Dr. Christopher always insisted, which is the way we have been eating. [EWH p.125] Potassium sources: There are several ways to receive your potassium. Dr. Bernard Jensen sells a potassium broth made from dehydrated vegetables. Dr. Bronner makes a similar, excellent product. You can also make your own potassium broth by simmering equal parts of red potatoes, celery, carrots, onions, and herbs to taste. Raw vegetable and fruit juices also flood the system with potassium. [EWH p.125]
Tips, Tips and More Tips by Anne J.B. Skinner (p. 103, 113)
There are very few studies that directly tie diet and mineral deficiencies to immune system function. So it's likely there is no scientific evidence that banana peels or vinegar (ACV) is an effective treatment for wart removal.
Here is one which I've found close enough: Evaluation of Topical Potassium Hydroxide Solution for Treatment of Plane Warts and the conclusion was:
Topical KOH solution is proved to be an effective and safe treatment of plane warts in both concentrations (5% and 10%) with no important side effects.