Al-jawab billahi at-taufeeq (the answer with Allah's guidance)
It is recommended to place a barrier (Sutra) in front when praying, if one thinks that someone may pass in front of one. [Shurunbulali, Maraqi al-Falah]. However, It will be Makruh if one does not place the Sutrah if one thinks that someone will pass. (Nurul Idhah pg. 89).
This doesn't affect the validity of one's prayer: if someone walks by, one's prayer remains valid. It is Mustahab not to stop the one who walks in front of one's prayer. However, permission is given to stop the passer by Isharah (gestures) or Tasbeeh and it is Makruh to combine both. (Nurul Idhah Pg. 89, 90)
It is sinful to walk immediately in front of someone praying when it is easy to avoid. (Aapke Masaa'il Aur Unka Hal Vol. 2 Pg. 294)
