The phrase "thank you for your concern" is correct and can be used in written English. It can be used when someone has expressed worries or anxieties about a particular situation, and you want to acknowledge and appreciate those feelings. For example: "I understand your worry about my low grades, thank you for your concern.".
Thank you for your concern and thanks for the memories, but Adios!
Thank you for your concern".
"It was only a sigh, but thank you for your concern".
"As far as the direction of the statue," she continued, "I thank you for your concern on this matter.
The leader of Oxfordshire County council writing to Cameron: "Thank you for your concerns about local government cuts but I regret to inform you that your constituency is no longer in Oxfordshire due to electoral boundary changes which your government implemented"?
"People who worry I may get hurt, I thank you for your concerns.
Thank you for your concerns, but my vitals are good for now.
I love the desktop app, it’s always running on my Mac. Ludwig is the best English buddy, it answers my 100 queries per day and stays cool.
Cristina Valenza
Retail Lead Linguist @ Apple Inc.