You know like Muslims when they do namaz they take their shoes off, how come they don’t take their shoes off when they are doing du’a? Because du’a is not a formal prayer, shoes are taken off, du’a can be said anywhere, in the mosque, outside the mosque, walking in the street, in fact you can constantly pray, so it is impossible for you, the moment you start making du’a to take your shoes off, wherever you are, in the street, anywhere, so God has not loaded you with responsibilities which you cannot discharge, but if you want to say du’a in the mosque, even if you don’t want to say a prayer but you enter the mosque, out of respect for the mosque, out of consideration for keeping the mosque clean, you take your shoes off, but for du’a you don’t have to bow, you don’t have to prostrate, so there is no need for any clean place at all.
And remember that when we go to say the prayer in the mosque, while saying the formal prayers, we prostrate by touching our forehead to the ground, to the floor, and if you were permitted to take your shoes into the mosque, the whole place would be so filthy and full of germs and infections of all sorts, that it is very likely that every Muslim would carry some eczema or some other skin disease on the forehead, so it is fortunate that God has forbidden us to walk into the mosque with shoes on, right?