Pesticides can and do sometimes penetrate banana skin.
The banana peel acts as a barrier although some pesticides such as the systemic pesticides can move across the banana peel and into the edible flesh of the banana.
Systemic pesticides are designed to be absorbed into the plant and are much more likely to penetrate the banana peel than contact pesticides.
Pesticides can move through the banana peel through lateral penetration and vertical migration, and could potentially reach the inner core of the banana over time.
If concerned about pesticides you can opt for organic bananas which are grown without pesticides although they may contain some natural pesticides which are less harmful.
Organic bananas are grown without synthetic pesticides, although organic bananas may still contain some trace amounts of naturally derived pesticides.
Organic farming practices for organic bananas do allow for the use of some certain natural pesticides, although they are still regulated and also used cautiously when growing organic bananas and other organic fruits and vegetables.
So organic bananas are often lower in pesticide residues when compared to non organic bananas, but they are not completely pesticide free.
Growing of regular and non organic bananas often involves the use of synthetic pesticides, herbicides and even fertilizers.
Although organic banana production and farming prohibits the use of fertilizers and synthetic pesticides, but they can use naturally derived pesticides.
Organic farmers of bananas and other fruits and vegetables can also use pesticides that are derived from natural sources like copper sulfate or other naturally occurring substances.
Although these natural pesticides are still monitored and regulated, but they can still be present in small amounts of organic produce and fruits and vegetables including bananas.