Sheikh `Abd al-Rahmân al-`Ajlân, lecturer at the Grand Mosque in Mecca
Rinsing the mouth (madmadah) and cleaning the nose by inhaling and exhaling water (istinshâq) are obligatory acts for both wudû’ and ghusl. This is because washing the face is obligatory in both wudû’ and ghusl and these acts constitute part of the washing of the face.
This is the position of Ahmad b. Hanbal and the official ruling of the Hanbalî school of thought. A number other scholars have adopted this opinion as well. This is the strongest opinion.
However, there are other scholarly opinions on this matter.
It has been related from Ahmad b. Hanbal that cleaning the nose by inhaling and exhaling water (istinshâq) is obligatory but rinsing the mouth (madmadah) is not.
A third opinion held by scholars is that both of these acts are obligatory in ghusl but neither are obligatory for wudû’.
Another opinion is that neither of these acts are ever obligatory; rather they are Sunnah practices for both wudû’ and ghusl. This is the ruling adopted by the Shâfi`î and Mâlikî schools of law.
It is not necessary for a person who forgets to clean his mouth and nose to perform the ghusl over again. It would be enough for him to simply rinse the mouth and nose. This is because it is not required while performing ghusl to carry out all of its actions in a particular sequence or without interruption, as long as this ghusl is being performed as purification from janâbah.
And Allah knows best.
Source: Islam Today