Well the answer seems to be in negative if the use has not been preventively authorized by The Holy See. In a statement recently, the Secretariat of state, warned against unauthorized use of and misuse of image of Pope Francis:
“The Secretariat of state includes among its responsibilities the protection of image of Holy Father, so that his message may reach faithful intact, and so that his person is not exploited. For the same reason, the Secretariat of the State, safeguards all symbols and official coats of arms of the Holy See via the appropriate regulatory instruments at international level. To render this protection increasingly effective for the aforementioned purpose and to stop any illegal situation that may arise, the Secretariat of the State carries out systematic surveillance activities to monitor the way in which the image of the Holy Father and the coats of arms of the Holy See are used, taking appropriate action where necessary.”
Legal grounds for cease-and-desist letters sent in this specific instance?
Canon law, and the laws directly adopted are the primary source of the law for the Vatican, whose legal system, also confirm the general principle of international law, as well as the provision included in the main international treaties, and agreements to which The Holy See is a party. However, for civil matters in respect of which there is no specific Vatican law, as long as they are compatible with Vatican laws and principle of canon law, and excluding a number of areas.

Protection Provision

Article 10 states:

“if image of a person, their parents, their spouse or their children is used or published outside the cases in which use or publication is allowed by the law, or in a way, in which to cause prejudice to the honor or reputation of person themselves or their said relatives, upon request of the person, can repress the violation and order payment of damages.”

“Standing the provision on the protection of distinctive signs and patents, anyone who commits any of the following is liable for unfair competition:

  1. Uses names or distinctive signs that are likely to be confused with the names or distinctive signs lawfully uses by others , or slavishly imitates the product of a competitor, or with any other means commits acts that are likely to create confusion with product and activity of the competitor;
  2. Divulges information on or reviews of the product and activity of a competitors, that are likely to discredit or misappropriate the qualities of the product or activity of a competitor;
  3. Uses directly or indirectly any other means that does not comply with principles of professional fairness and is likely to harm third party activities.”