Praise be to Allah.
When the one who joined the prayer late gets up to complete his prayer, he does not have to move from his spot in order to pray behind a sutrah, or to do what you mentioned of letting other worshippers pass easily, because there are no religious texts which indicate that.
Shaykh Ibn ‘Uthaymin (may Allah have mercy on him) was asked: Sometimes a worshipper misses one or two rak‘ahs, and when the imam says the salaam, he finds that the sutrah is far away from him, two or three steps away. Is it permissible for him to step forward towards the sutrah?
He replied: What appears to me to be the case, based on the actions of the Sahaabah, is that the one who joined the prayer late does not have to have a sutrah in front of him, and he may make up what he missed of the prayer without a sutrah."(Liqa’ al-Bab al-Maftuh 232/30).
Undoubtedly having a sutrah for one who is praying is more important than making it easy for worshippers to get past him.
When the one who joined the prayer late gets up to complete his prayer, he comes under the ruling of one who is praying on his own, so he should prevent anyone from passing directly in front of him, and it is not permissible for anyone to pass directly in front of him. The one who wants to exit should show a little patience, or look for another place in which he can exit without disturbing those who are praying or passing directly in front of them.
And Allah knows best.