Because Anne Marie is a Queen (even if former), whereas Harry and William are just Princes. Or, in other words, protocol, respect.
For the same reason, Kate curtseys to Crown Princess Margarita of Romania, Queen Anne Marie, and other royal ladies from former monarchies.
Current monarchies tend to be much more uptight when it comes to former royal houses; as far as they are concerned, once a King - always a King. You might have noticed how in the official portrait taken before the Lunch for Monarchs, former Sovereigns (Michael of Romania, Simeon of Bulgaria...) were given great prominence - greater, in fact, than reigning ones for they were seated immediately next to the Queen. That's because as far as Royal Families are concerned, Michael and Simeon have been Kings since 1927 (1940) and 1943 respectively, and the fact their countries are no longer monarchies is somewhat irrelevant.