Is merely caring about what people say considered a sin of the heart, or does it have degrees, such that it is forbidden if it leads to what is forbidden, and disliked if it leads to what is disliked? And is the proposed therapeutic program to get rid of this concern correct?

Concern for what people say is not entirely blameworthy. A Muslim is required to avoid suspicious matters and preserve their reputation. Concern for what people say becomes blameworthy if it is for the purpose of pleasing them, or if it leads to disobeying Allah's command, such as committing a sin out of fear of their disapproval. A Muslim must prioritize shyness before Allah over shyness before people, and know that whoever pleases Allah, even if it displeases people, Allah will be pleased with him and make people pleased with him. And whoever displeases Allah to please people, Allah will be displeased with him and make people displeased with him. What is blameworthy of this concern must be abandoned.