Is there any specific virtue mentioned regarding the recommendation of performing 'Umrah in the month of Rajab?

There is no special virtue reported for 'Umrah in the month of Rajab, and the Prophet, peace and blessings be upon him, did not perform 'Umrah in it. Rather, 'Aishah denied that he did. Designating Rajab for 'Umrah is an innovation, because it is not permissible to designate an act of worship to a time that the Shari'ah has not designated. However, there is no harm in performing 'Umrah during it if there is no belief in a special virtue, but rather it happens by chance or due to ease of travel.