As a rule of thumb, feel free to send a thank-you note whenever the impulse strikes you. But a thank-you card (or a thank-you gift) sent to you is already a token of appreciation, so putting in yet more effort into thanking somebody for thanking you is purposeless, irritating even. It’s kind of morally superfluous.
Now, failing to acknowledge a thank-you note is a universal annoyance. By all means, you can text them, “Got your note. I’m glad you had a good time,” or inform them the next time you run into them in the hallway. However, no need to perpetuate a recursion of thank-you notes.