Domestic cats don’t really understand the human concept of saying thank you but in their own way they say it. It is more an action of reinforcing friendship than an out-and-out thank you.
When I feed my cat the best food I can get him, before I can open the food and place it in his bowl, he rubs his head on my hand. It is a sort of mini-head butt. This is feline behaviour in anticipation of receiving food. It is non-verbal and it is a sign of friendship. To me it is a “friendship behavioural exchange”. In giving him food I am demonstrating my friendship for him. In response he demonstrates his friendship for me by rubbing against me.
The way I see it, a physical demonstration of friendship is a way of acknowledging the friendship and its value. In doing this a cat is telling us that he enjoys the relationship and in doing so we can deduce that he is thankful for it.
This then is a subtle thank you for providing nice food.
This is a very short post because I don’t believe I can add to that except for one thing: there is discussion on the subject of whether cats understand “friendship”. I think cats do but scientists might prefer the word “associates” meaning that some cats get along and like each other’s company. As we are seen as a cat by our cat, we are then an associate but I prefer the word “friendship” which can be deep and enduring.