While it's not shown, it's hinted to have happen during the Fisher Tiger escape incident
The guy in the middle here seems to be Shanks before the incident(shorter hair than Shamrock)
During the incident, we see Shanks(with bandage) aiming for Fisher's neck collar and thus freeing him, with Fisher removing his bandage during the moment, and his eye bleeding(so fresh injury)
And when you add Shamrock's dialog later about it being more wise for Shanks to wait for his injury to heal, it's pretty clear Blackbeard scarred him during that incident
But the question is, what was Blackbeard doing there