Is it permissible for a group of women to perform Umrah together without a mahram, while it is not permissible for them to visit Medina except with a mahram? And what is the wisdom behind this difference?

It is permissible for a woman to travel for obligatory Hajj or Umrah with a trustworthy group, but it is not permissible for her to travel with a trustworthy group for a permissible or supererogatory journey. This is because traveling to Mecca is obligatory for performing Hajj and Umrah, whereas traveling to the Prophet's City (Medina) is not obligatory for her.