It's an intentional joke. The sentence is supposed to be impossible to understand. It has too many layers to it.
"Of course I care about how you feel." <---Makes sense.
"Of course I care about what you thought of my feelings." <---Makes sense.
"Of course I care about what you thought of my perception of your feelings." <---Getting hazy.
It's like one of those chains of reasoning in which you say "He'll expect me to do A, so I'll do B." And then you say "Well, he's really clever, so maybe I can fool him by doing what he expects, because he expects me to do what he doesn't expect," and so forth and so on.
I don't think it's very funny, by the way, and I don't really "get" it. I think the idea is that this couple has been arguing so long that they have gotten deeper and deeper into debating his feelings about her feelings about his feelings about her feelings.