Googling said this:
Yes, most banana peels contain some pesticide residue. However, the banana peel protects the edible part of the fruit from many chemicals, so the amount of pesticide residue on the fruit itself is usually low. 
Here's some more information about pesticides on bananas:
- Pesticide use
 Banana farmers use a lot of pesticides, with the Environmental Working Group estimating that they use 35 pounds per acre.
 
 
- Common pesticides
 Thiabendazole is the most common pesticide residue found on bananas, appearing in 48.1% of bananas tested.
 
 
- Safety
 The United States Department of Agriculture sets pesticide limits for safety, and most fruits do not exceed these limits. Touching a banana peel with pesticide residue is not harmful.
 
 
- Organic bananas
 Organic bananas are less likely to have traces of pesticides because organic farmers use fewer pesticides, or none at all.
 
 
- Washing
 If you want to eat a banana peel, you can wash it under running water.