How should I respond to someone who congratulates me on my birthday, knowing that it is not permissible to congratulate on birthdays?

The matter is as the questioner stated, regarding the prohibition of celebrating birthdays and congratulating on them. Therefore, it is not permissible to return the greeting in a way that implies satisfaction or affirmation of it. Rather, one should advise the congratulator and clarify the ruling on congratulating, in accordance with the hadith: "Religion is [sincere] advice."