I have only gotten one reply from Princess Caroline previously, for her 60th Birthday in 2017. (I did also get one letter returned to sender.)
I have only written to her on two occasions recently for Christmas (2022) & her birthday in January. The cards inside do not specify what event the reply was for. But I assume this is for those two events, and that her office just accidently sent a extra reply.
The envelopes were the same as Princess Caroline's past reply, featuring a real stamp and the Postmark stamped on all letters during that week.
Palais de Monaco
H.R.H. The Princess of Hanover would like to thank you for your kind wishes which were much appreciated.