Husband Had A Stroke 4 Months Ago And A Trackiotomy

Husband had a stroke 4 months ago and a trackiotomy for about 6 weeks. Since it was removed he has had a very bad hacky cough. His rehab centre say his chest is clear and so are his ears and he has only had linctus that was a waist of time. They are now speculating it's the food he eats. The irritation seems to be at the back of the mouth. What might it be