Is the reward for prayer reduced by half if one does not have a sutrah?
Question

Is there a hadith which says that praying without a sutrah reduces the (reward for) the prayer to half? 
 
If there is such a hadith, please tell me the name of the narrator and who transmitted it.
Praise be to Allah.We have not found any hadith from the Prophet (blessings and peace of Allah be upon him) to suggest that the reward for a prayer offered without a sutrah in front of the worshipper is reduced by half. It is most likely that this is the opinion reached by one of the scholars. Many hadiths have been narrated enjoining use of a sutrah and praying facing towards it, and warning against the shaytaan interrupting the prayer if one prays without a sutrah. 
It was narrated from Sahl ibn Abi Hathmah that the Prophet (blessings and peace of Allah be upon him) said: “If one of you prays facing a sutrah, let him draw close to it and not let the shaytaan interrupt his prayer.” 
Narrated by Abu Dawood (number 695); classed as hasan by Ibn ‘Abd al-Barr in al-Tamheed (4/1505); classed as saheeh by al-Nawawi in al-Majmoo’ (3/244); classed as saheeh by al-Albani in Saheeh Abi Dawood. 
Al-Azeemabaadi (may Allah have mercy on him) says:
i.e., so he will not be distracted by whispers from the shaytaan. It may be understood from this that the sutrah prevents the shaytaan from taking over the worshipper and instilling his whispers into his heart, either completely or partially, according to the worshipper's sincerity and his focusing and turning to Allah in his prayer. If there is no sutrah then the shaytaan can cause him to fail to pray with proper focus and humility. End quote. 
‘Awn al-Ma’bood (2/275). 
Perhaps the one who said that the reward for prayer of one who prays without a sutrah is reduced was referring to this meaning, especially if someone walks in front of him and interrupts his prayer. In that case the one who walks in front of him is sinning and the one who was praying is affected by the distraction from his prayer because of his shortcoming. 
Ibn Hajar al-Haytami (may Allah have mercy on him) said: 
It may be understood as referring to interruption of the prayer by someone walking in front of him and distracting him, which is mentioned in the hadiths: interruption of khushoo’ (proper focus) and the harm resulting from being distracted by the one who walks in front, and the shaytaan being able to get control of him by whispering and distracting him from what he is doing so that he does not understand anything of his prayer or anything except a little, so he misses out on the reward. All of that is what is referred to in the hadith in which the Prophet (blessings and peace of Allah be upon him) says: “and not let the shaytaan interrupt his prayer” 
Al-Fataawa al-Fiqhiyyah al-Kubra (1/170) 
This also explains what was narrated from Ibn Mas’ood (may Allah be pleased with him) when he said:
If anyone wants to walk in front of you when you are praying, do not let him, for he will make you lose half of your prayer. End quote 
al-Musannaf (2/25) with an isnaad which includes a unknown narrator. 
It is also the meaning of what was said by some of the salaf such as Abu Ishaaq and Yahya ibn Abi Katheer, that it is not appropriate to pray without a sutrah. This was narrated by Ibn al-Mundhir in al-Awsat (no. 2395), and a similar meaning is found in a report narrated by ‘Abd al-Razzaaq in al-Musannaf (2/26), Bab man salla ila ghayri sutrah. 
Whatever the case, the scholars are agreed that prayer without a sutrah is still valid, even though the reward for it is less than that of one who prays facing a sutrah. But there is no report which indicates that this detraction is as much as half of the reward. 
Ibn Hajar al-Haytami (may Allah have mercy on him) said: 
If a person prays without a sutrah when he is able to do so, there is no difference of opinion concerning the fact that his prayer is valid.  
Al-Fataawa al-Fiqhiyyah al-Kubra (1/160). What is meant is that the scholars are unanimously agreed that his prayer is valid. End quote. 
For more information on the ruling on the sutrah, please see the answer to question number 117758.  
And Allah knows best.