As soon as the image arises, reject it. Give it no energy whatsoever. At first, some sorrow will be triggered. But pretty soon, the mind seems to recognize what's going on, and even sorrow does not arise. This is not denial, surely.
Denial is the refusal to acknowledge the truth or reality of an event or relationship or whatever.
This is not about that. Notice that it's not the absence of our four-legged friend that generates sorrow, but the memory of her. In other words, the pain which these memories trigger is somehow almost pleasant. Surely, it is the ego, the separative personality. And anything that reinforces our sense of separateness serves the ego.