If the gesture is made in a cordial way and you realize it is really your fault, then accept your fault and say, "My apologies, I stand corrected. Thank You." It's usually when someone corrects my pronunciation. My favorite reply is that language is a medium of communication.
Depending on the situation, it would be better to say or write, “Thank you for providing me with the correct information” (less concise, but neutral in tone) or “Thank you for clarifying that for me.” In American English, at least, an informal, friendly way to acknowledge correction is “Thanks for setting me straight.”
