Kate was seen leaving Windsor Castle with husband William, 41, as he went to Westminster Abbey for the Commonwealth Day service.
It is understood that she did not attend the service and was believed to be heading to a private appointment instead.
The princess, 42, issued her apology on social media after photographic agencies withdrew the official family image released by Kensington Palace, dismissing it with a "kill" notice after discovering it had been altered.
In her statement, Kate said: "Like many amateur photographers, I do occasionally experiment with editing.
"I wanted to express my apologies for any confusion the family photograph we shared yesterday caused. I hope everyone celebrating had a very happy Mother's Day. C."
But not everyone agreed she needed to apologise. Royal commentator Dickie Arbiter said: "All the fuss created over a simple family photograph is just a lot of nonsense.
"At the end of the day, what you have is a Princess with honesty and integrity coming out and saying, 'Sure, I edited this picture'.
"Instead of apologising for it, she should just have said: 'So what?'."
And former BBC royal correspondent Jennie Bond branded the affair a "storm in a teacup".
She added: "It is unfortunate. The Princess herself has said she's been in an amateurish way trying to edit her picture. She's made a right mess of it.
"The result is a storm of ridiculous speculation about the true state of her health.
Embarrassed
"I'm sure she's mightily embarrassed about it, particularly because it's overshadowed a very big day for the Royal Family, the Commonwealth Day ceremony at Westminster Abbey.
"I'm sure she's feeling very contrite and I'm sure it's ruined her Mother's Day. I don't think it is seriously damaging."
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