Princeton LoR Deadline

Hi all!

I'm applying for Princeton MFin program whose deadline is Jan 3, 2022.

One of my recommenders is travelling and said that he won't be able to submit the LoR before 10 Jan.

I got in touch with the Princeton admissions team who said, "it is highly recommended that they submit their letters on or before the application deadline as the review board is allowed to begin reading applications immediately after the deadline. If your recommender waits too long after the deadline to submit, you run the risk that the board will review an incomplete application."

Will 1 week make a huge difference as I have seen many other programs accept LoRs till 2 weeks after the deadline? Was anyone else in a similar position, particularly wrt Princeton? If yes, how was your experience?