Question Summary:
Kissing the Hajr Aswad which has itr on it

Question Detail:

If you kissed the Hajr Aswad while in ehraam and the itr that people put on it touched your lips and hands. Do you give dhamm or sadaqah?

Answer :

In the Name of Allah, the Most Gracious, the Most Merciful.
As-salāmu ‘alaykum wa-rahmatullāhi wa-barakātuh
According to Shariah, the limbs of the human body are of two types:

 
If itr touches a big limb, one is required to give damm. (Damm refers to the slaughtering of a goat, a sheep or one-seventh part of a cow or a camel within the precincts of the Haram). If itr touches a small limb, one is required to give Sadaqah (Sadaqah is 1.75kg to 2.32 kg/3.86 lb to 5.11 lb of wheat or its monetary value which is equal to the amount given for Sadaqat-ul-Fitr).  
 
Shariah considers the hands and palms as big limbs. Therefore, one is required to pay Damm if itr touches the entire hands and palms. However, there is a difference of ruling when itr touches a small portion or most of the hands and palms. In such a case, one is required to give Sadaqah.
 
As far as the lips are concerned, one is required to give Sadaqah if itr touches the entire lips.
However, the above mentioned rulings will only apply when a small amount of itr was touched. Whereas if a large amount of itr touches any limb of the body, Damm will be binding upon the person. [i]
Bear in mind, once the itr touches the body, it is necessary to remove or wash it off immediately. If the penalty was given and the itr was not removed or washed off, a second penalty will be binding upon the person. [ii]
And Allah Ta’āla Knows Best
Fahad Abdul Wahab
Student Darul Iftaa
U.S.A 
Checked and Approved by,
Mufti Ebrahim Desai.