Warts only seem to form when your immune system deems them "below threshold".
Presumably, the continuous irritation from the duct tape causes your immune system to say "Oy, there is irritation here. Go find the source and stop it." At some point, your immune systems notices "Hey, there's a virus here that we weren't paying attention to. Let's get rid of that."
There are stories of people who talk about how they had a couple of warts and then "something" injured one of them such that blood came out and suddenly all their warts disappeared simultaneously. Presumably their immune system "noticed" and then cleared the virii out systemically.
Presumably, the continuous irritation from the duct tape causes your immune system to say "Oy, there is irritation here. Go find the source and stop it." At some point, your immune systems notices "Hey, there's a virus here that we weren't paying attention to. Let's get rid of that."
There are stories of people who talk about how they had a couple of warts and then "something" injured one of them such that blood came out and suddenly all their warts disappeared simultaneously. Presumably their immune system "noticed" and then cleared the virii out systemically.