To write the letter "p" with a circumflex (p̂) for an axis label in MATLAB, users can utilize the set function along with the 'XTick' and 'XTickLabel' properties. This method allows for custom labeling of graph axes, enabling the inclusion of special characters. The discussion highlights the importance of understanding how to manipulate axis properties in MATLAB to achieve the desired formatting for graph labels. Additionally, while ASCII codes were mentioned, the focus remains on using MATLAB's built-in capabilities for special character representation.