Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is permissible to make up missed prayers at any time even at the times when praying is disliked.
Answering your question, Dar Al-Ifta Al-Misriyyah, states:
It is permissible to make up missed prayers at any time even at the times when praying is disliked.
It is forbidden to perform supererogatory prayers at the times in which praying is disliked, and this also applies to the Sunnah prayer of ihram [state of pilgrim sanctity] and the istikharah [prayer for guidance and seeking a choice] prayer.
However, there is no harm in offering prayers in Makkah during those times.
Almighty Allah knows best.
Source: http://www.dar-alifta.org/Foreign/ViewFatwa.aspx?ID=7962