Alvis' first priority is the safety of / loyalty to the kingdom - no matter his sense of justice. And that makes sense.
The most ridiculous thing so far is that the priest decided to simply immobilise and abandon her in the forest instead of directly killing her. There must have been some method of killing her that's both discrete and decisive. Now, him half-assing it is going to result in his undoing later in the future since she's still alive.