The Elder of Zion blog reported that "the original photographer/artist is Mikhail Levit," and noted that the photo has been on websites as far back as 2008: "So obviously the IDF rabbinate did not edit the photo. It was a nice picture; the people behind the pamphlet found it somewhere online, and put it on the pamphlet."The link in the article to the Elder of Zion blog post doesn't work, but you can read it here.
A reserves officer who brought the photo to Haaretz's attention warned that “A world war could break out if someone tried to do something about that place," and opined that the Rabbinate "should be more cautious when approaching the subject.”
However, it was precisely the publication in Haaretz that drew jihadi and international attention to the story.
It seems then that the publication of the photo in the pamphlet may have been a careless mistake. Someone thought it was a nice photo and somehow didn't notice the Dome of the Rock was missing. Such things happen happen from time to time and are embarrassing, but are not that big a deal.
But if this is the explanation, the IDF handled the situation poorly by claiming the photo was meant to show the Temple Mount in the time of the Second Temple instead of just 'fessing up to the mistake. The explanation is ridiculous and implies a complicity that is unhelpful.
Whether or not Haaretz should have published the article once the story came to their attention is another question. The writer of the blog post is sharply critical. I'm inclined to cut them a little slack, since Haaretz does make some effort (not without errors) to be evenhanded on the subject of the Temple Mount, covering issues like the Waqf's illicit excavations there and the work of the Temple Mount Sifting Project (see, e.g., here and links). It's the job of the media to keep governments on their toes, and that means publicizing their silly mistakes. I don't think the reaction or over-reaction of jihadi websites is of that much interest either way.