Exercise is great, but don’t forget the facts about fat. Banting may be high in fat, but it is the sugars that result from a carbohydrate rich diet that makes you fat, cause inflammation and other diseases.
You are free to exercise while Banting - there are a whole host of benefits in doing so - yet it is not necessary for weight loss. Eating real food will help you trim down in no time! For more information about exercise and nutrition see "Why Some People Don’t Lose Weight When Banting" and Gary Taubes’ great video: "Why We Get Fat".