Charles, who wore a face mask for the occasion, gave a nervous chuckle and carried on walking.
Charles has been described as being in a "state of despair" over the interview, in which Harry said his father stopped taking his calls after he and Meghan decided to leave as working royals.
The Duke of Sussex said he felt "let down" by his father after he was cut off financially, but said he hoped to "heal" the relationship.
Harry also said he thought his father, the future king, had "made his peace" with the "toxic environment" of royal life.
Meghan and Harry sat down for an interview with Oprah Winfrey, which aired in the US on Sunday night on CBS.
The two-hour interview contained a number of bombshell allegations including that a — currently unnamed — royal made comments about Archie's skin colour that have been labelled as racist.
Harry and Meghan also revealed they had suffered mental health issues, with Meghan saying she contemplated suicide at one point.
The interview prompted crisis talks in Buckingham Palace and the Queen issued a statement today expressing her "concern".
"The whole family is saddened to learn the full extent of how challenging the last few years have been for Harry and Meghan," the Queen's statement said.
"The issues raised, particularly that of race, are concerning. Whilst some recollections may vary, they are taken very seriously and will be addressed by the family privately.
"Harry, Meghan and Archie will always be much loved family members."
Harry and Meghan withdrew from royal duties in 2020 when they announced their decision to "step back as 'senior' members" of the royal family and spend their time living between the UK and North America.
