There is no report from the Prophet (peace be upon him) as to suggest that there is any special virtue in performing umrah in the month of Rajab or that it is encouraged.
The virtue of performing umrah in the month of Ramadhan and in the months of Hajj i.e. shawaal,Dhul Qadah and Dhul hajj are however proven.
There is no report to prove that the Prophet (peace and blessings of Allaah be upon him) performed ‘Umrah in Rajab, rather that was denied by ‘Aa’ishah (may Allaah be pleased with her), who said: The Messenger of Allaah (peace and blessings of Allaah be upon him) never performed ‘Umrah in Rajab. Narrated by al-Bukhaari, 1776; Muslim, 1255.
Singling out the month of Rajab for Umrah is something that is introduced by people. No one should do that and single out a specific time for doing an act of worship unless that has been prescribed in shareeah or is proven in Sunnah of Prophet Muhammad(peace be upon him).
Ibn al-‘Attaar, the student of al-Nawawi (may Allaah have mercy on them both) said:
What I have heard about the people of Makkah, may Allaah increase it in honour, is that they are accustomed to performing ‘Umrah a great deal in Rajab. This is something for which I know of no basis, rather it is proven in the hadeeth that the Prophet (peace and blessings of Allaah be upon him) said: “ ‘Umrah in Ramadaan is equivalent to Hajj.”
Performing acts of worship at specific times believing that those times are virtuous is not right because no time is better than what is already prescribed un shareeah.
Also all the scholars denounced the singling out of the month of Rajab for performing ‘Umrah a great deal.
But if a person goes for ‘Umrah during Rajab without believing that there is any special virtue in that, but it just so happens that it is easy for him to travel at that time, there is nothing wrong with that.
And Allah knows best.