Praise be to Allaah.
It is not permissible to throw papers containing mention of Allah, may He be exalted, on the ground because that is showing disrespect towards the name of Allah and not venerating His name.
The duty of the Muslim who feels proud of his religion and who respects the symbols of his Lord with regard to this matter includes a number of things:
He should not handle with disrespect any paper on which there is mention of Allah, by throwing it on the ground or sitting on it or using it to eat food from and so on.
He should advise his Muslim brothers not to throw away any paper that contains mention of Allah.
He should pick up from the ground any papers that have been dropped on which there is mention of Allah or hadeeths of the Messenger of Allah (blessings and peace of Allah be upon him), then he should burn them or bury them in clean ground far away from where people walk.
He does not have to look at every piece of paper that is on the ground to see what is in it, but he does not have to pick up every piece of paper on the ground on which there is any mention of Allah, because that would cause a great deal of hardship for him. All that is required of him to do in this regard is what he is able to do, without putting himself through hardship and difficulty.
There follow some of the fatwas of the scholars concerning this matter:
Shaykh Ibn Uthaymeen (may Allah have mercy on him) said:
If it is known that these newspapers contain verses of the Qur'aan or names of Allah, may He be glorified and exalted, or hadeeths of the Messenger of Allah (blessings and peace of Allah be upon him), then it is not permissible to use them for food or sitting on them and so on, because that is a kind of disrespect towards the words of Allah and His names and the hadeeths of the Prophet (blessings and peace of Allah be upon him). End quote from Fataawa Noor ala al-Darb by Ibn Uthaymeen, 13/59
The Standing Committee for Issuing Fatwas was asked:
What is the duty of the Muslim towards pieces of paper on which there are Qur'aanic verses and hadeeths of the Messenger (blessings and peace of Allah be upon him) that are dropped on streets and sidewalks?
If it can be seen that the piece of paper contains a verse from the Book of Allah or a hadeeth of the Messenger of Allah (blessings and peace of Allah be upon him) or any mention of Allah, may He be glorified and exalted, or the Sunnah of His Messenger (blessings and peace of Allah be upon him, or any of the names and attributes of Allah - then he should pick it up and burn it or bury it in clean ground that is not where people walk. He should not throw it on the ground, because that is regarded as showing disrespect to the Book of Allah, may He be glorified and exalted. End quote from Fataawa al-Lajnah al-Daa'imah, 3/42
The Committee was also asked:
I often see clippings from newspapers and magazines on the streets and sidewalks, and when I examine them I find that they contain the name of Allah and Qur'aanic verses. If I see those newspapers and magazines, do I have to stop whilst I am driving my car and collect these pieces of paper?
They replied: If you see any papers from the streets or elsewhere on which there is any mention of Allah or anything of the Qur'aan, you have to pick it up and move it from a place of disrespect to a place where it will be protected, or burn it.
End quote from Fataawa al-Lajnah al-Daa'imah, 3/40
The Committee was also asked:
Should I walk through the streets bending over to pick up these verses and soorahs which are often thrown on the ground, when the people make fun of me? What should I do to remove this widespread evil?
Firstly, it is not permissible for the Muslim to wrap his goods or merchandise in papers on which soorahs or verses of the Holy Qur'aan, or hadeeths of the Prophet (blessings and peace of Allah be upon him) are written, or to throw papers on which such things are written on the streets or in neighbourhoods or unclean places, because that is a kind of disrespect and transgressing against the sanctity of the Qur'aan, Prophetic hadeeths and remembrance of Allah.
Secondly: it is sufficient, in order to avoid sin and blame, to advise people not to use the papers mentioned in ways that are disrespectful, and to advise them not to throw these things into trash cans or on the street and so on. You are not obliged to do that which causes hardship for yourself by making yourself pick up all these things that scattered in the streets and the like. Rather you should pick up whatever you are able to do of such things without causing yourself difficulty or hardship.
End quote from Fataawa al-Lajnah al-Daa'imah, 4/74-75
All you have to do with regard to this matter is whatever you are able to do and whatever is easy for you to do without making it difficult for yourself.
And Allah knows best.