All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is not obligatory to wash the inner part of the eyes during the ablution, and it is not even recommended. If the person has applied Kohl (eyeliner) to his/her eyes, he/she is not obliged to remove it from the inside of the eyes before performing ablution. While performing ablution, the inside of the eyes should not to be washed to remove the Kohl.
As for the Kohl applied to the outer parts of the eyes, if it is merely a color like ink or the like, there is no harm in that and this does not affect the validity of the ablution. However, if the layer of the Kohl is thick and prevents the water from reaching the skin, it is obligatory to remove it before the ablution.
Ibn ‘Uthaymeen was asked about whether Kohl prevents water from reaching the skin during ablution or not. He answered, “If it is like ink or similar [substances with color], it does not prevent water from reaching the skin even if it is somehow washed away when applying water. However, if it is has a mass or is a thick layer that prevents the water from reaching the skin, it should be removed before the ablution.”
Now you should know the guideline to distinguish between what obstructs the water from reaching the skin and therefore has to be removed and between what does not.