The tradition mentioned above has also been transmitted by Ya'la b. Umayyah through a different chain of narrators. This version has:
The Prophet ﷺ said to the man bit him: If you wish that you give him control over your hand and he bites it, and then you drive it away from his mouth (you may do it). He imposed no retaliation for his teeth.

حَدَّثَنَا زِيَادُ بْنُ أَيُّوبَ، أَخْبَرَنَا هُشَيْمٌ، حَدَّثَنَا حَجَّاجٌ، وَعَبْدُ الْمَلِكِ، عَنْ عَطَاءٍ، عَنْ يَعْلَى بْنِ أُمَيَّةَ، بِهَذَا زَادَ ثُمَّ قَالَ يَعْنِي النَّبِيَّ ﷺ لِلْعَاضِّ " إِنْ شِئْتَ أَنْ تُمَكِّنَهُ مِنْ يَدِكَ فَيَعَضَّهَا ثُمَّ تَنْزِعَهَا مِنْ فِيهِ " . وَأَبْطَلَ دِيَةَ أَسْنَانِهِ .