Performing উমরাহ in Dhul Hijjah is permissible according to all scholars, as there is no prohibition against উমরাহ in any month of the year. The first ten days of Dhul Hijjah are among the best days of the year, and performing উমরাহ in them is virtuous. The question that generates more discussion is performing উমরাহ after completing হজ্জ, during the remaining days of Dhul Hijjah.
Sheikh Ibn Baz stated that performing উমরাহ after হজ্জ is permissible, as demonstrated by নবী করীম's instruction to Abdur-Rahman to take his sister Aisha to Tan'eem for উমরাহ after their হজ্জ was complete. This occurred during the Farewell Pilgrimage in Dhul Hijjah. He considered this a clear evidence that উমরাহ in Dhul Hijjah — even after হজ্জ — is valid and carries reward.
Sheikh Al-Albani, however, noted that Aisha's উমরাহ was a special case — she was distressed because she had not been able to perform a separate উমরাহ (having been instructed to combine হজ্জ and উমরাহ as qiran). নবী করীম accommodated her specific situation. He pointed out that নবী করীম himself and the rest of the companions did not perform উমরাহ after হজ্জ. Based on this, Al-Albani considered it better to follow নবী করীম's own practice of not performing a separate উমরাহ after হজ্জ, though he did not prohibit it.