That was months later.
Kirk could only suspect if Kurge was under Orders to steal Genesis.
I don't think we can speculate as to the time delay or Klingon intention unless it is stated in otherwise canon material..
If Kruge had been rogue or acting without instruction they could have easily claimed that he was not acting in the name of the Empire and was not authorized to do as he did. Instead the Empire doubled down and was unapologetic.
In the original draft of TSFS Kruge was rogue, had stolen a *Romulan* Bird of Prey and was acting on his own. But that isn't what came to the screen.