The phrase "to heal the breach" means to fix or mend a broken relationship or disagreement between two parties. It's about bringing them closer together and resolving any issues, misunderstandings, or conflicts they may have had. Full definition
Agatha and James heal their breach in the Vatican (she is there on a New Year's tour of Italy), a small town that is a universal city. (firstthings.com)
Now, according to Archbishop Guido Pozzo, a senior Vatican official involved in discussions with the Lefebvrists, it may be possible to heal the breach Archbishop Lefebvre created by conceding that the teachings of Vatican II do not all have the same doctrinal weight. (firstthings.com)
If, for example, the Lutherans and Roman Catholics succeed in «healing the breach of the 16th century» and just do it between themselves, where does that leave the other churches? (religion-online.org)