The Sun released a image of the couple on Saturday, claiming to have captured them wandering through a parking lot at Windsor Farm Shop, which is close to their residence.
Their three children, Prince George, age 10, Princess Charlotte, age 8, and Prince Louis, age 5, were not present.
The newspaper cited customer Nelson Silva, who captured the footage, stating that while Kate appeared “happy and relaxed,” they appeared “super relaxed.”
It was described as “just a woman shopping with her husband on a Saturday afternoon, just like thousands of other couples across the country” by a second eyewitness who saw the image.
The couple has been the subject of social media rumors in recent weeks.
Later, Kensington Palace verified that the procedure went well and that she would need some time to heal at home in Windsor.
The princess issued an apology earlier this month, saying she was sorry “for any confusion” caused when it became apparent that a Mother’s Day photo she had taken with her kids had been altered before being sent to photo agencies.