I wouldn’t reduce the adaptation to endurance training only to IL13. But for sure endurance training causes inflammation and stress on the body. Many different mediators are involved and lead to adaptation after recovery. There are some studies that suggest that this adaptation is impaired when you block the inflammatory response with medications or even ice baths and other things. As with most things, balance is key.
One of the key mechanisms in asthma is an inflammation of the bronchia (IL13 plays a key role). So one therapeutic option is to inhibit this inflammation. This can be done by corticosteroids (inhaled or even systemic) or by LTRA (Leukotriene-Receptor-Antagonists).
ICS are inhaled corticosteroids, so they act mostly on the lung. Only if you go beyond 1mg/d systemic effects are possible. This way (and also by oral administration) they would also suppress inflammation in the whole body (not only the lung). LTRA are taken orally, but they are far less anti-inflammatory.
Overall I don’t really see an adverse effect of the medications on endurance adaptations. It’s far more important that you control your asthma with the right medications so that you are able to train normally. From what I know there is no evidence that people who are on asthma medications have less adaptation to endurance training.
What’s your experience? What medications do you take?
I hope that helps!?